{"id":671,"date":"2022-02-13T06:18:48","date_gmt":"2022-02-13T09:18:48","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=671"},"modified":"2026-01-23T02:29:45","modified_gmt":"2026-01-23T05:29:45","slug":"recreation-of-numbers","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=671","title":{"rendered":"Work on Recreation of Numbers"},"content":{"rendered":"\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">1. General Work<\/mark> <\/h3>\n\n\n\n<p><\/p>\n\n\n\n<ol class=\"wp-block-list has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>, <em>2019 In Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 31, 2019, pp. 1-27, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2529103\">http:\/\/doi.org\/10.5281\/zenodo.2529103<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>2020 In Numbers: Mathematical Style<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 31, 2019, pp. 1-37, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.3596193\">http:\/\/doi.org\/10.5281\/zenodo.3596193<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Factorial-Type Numerical Calendar<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 24, 2020, pp. 1-33, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.3726335\">http:\/\/doi.org\/10.5281\/zenodo.3726335<\/a>.\n<ul class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Factorial-Type Numerical Calender 2021<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 16, 2020, pp. 1-31, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.4329889\">http:\/\/doi.org\/10.5281\/zenodo.4329889<\/a>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>21 Mathematical Highlights for 2021<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 26, 2020, pp. 1-75, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.4394408\">http:\/\/doi.org\/10.5281\/zenodo.4394408<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Geometrical, Numerical, and Symmetrical Representations for the Days of 2020<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 04, 2020, pp. 1-201,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.4065069\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.4065069<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Hardy-Ramanujan Number \u2013 1729<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 22, 2021, pp. 1-106, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.5799640\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.5799640<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Mathematical Beauty of 2022<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 26, 2021, pp. 1-78, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.5805264\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.5805264<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>23 and 2023 in Numbers and Patterns<\/em>, <strong>Zenodo<\/strong>, December 22, 2022, pp. 1-51, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.7473340\">https:\/\/doi.org\/10.5281\/zenodo.7473340<\/a>.<\/li>\n\n\n\n<li>Inder J. Taneja, Mathematical Representations of the Last Day of the Year 23 Written American Style: 12.31.23 (123123),&nbsp;<strong>Zenodo<\/strong>, December 19, 2023, pp. 1-13,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.10405771\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.10405771<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Mathematical Aspects of 24 and 2024,&nbsp;<strong>Zenodo<\/strong>, December 19, 2023, pp. 1-40, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10406530\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.10406530<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares,&nbsp;<strong>Zenodo<\/strong>, December 20, 2024, pp. 1-94,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.14533193\">https:\/\/doi.org\/10.5281\/zenodo.14533193<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Crazy, Single Digit, Single Letter and Pyramid-Type Representations for the Dates of the Year 25, <strong>Zenodo<\/strong>, March 12, 2025, pp. 1-388, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.15013279\">https:\/\/doi.org\/10.5281\/zenodo.15013279<\/a><\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,245,203) 0%,rgb(174,196,79) 12%,rgb(182,227,212) 50%,rgb(255,255,255) 65%,rgb(51,167,181) 100%)\">Site Links of General Work<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<ol class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\n<li><strong>Inder J. Taneja, <em>2019 In Numbers<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2018\/12\/31\/2019-in-numbers\/\">2019 In Numbers \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>2020 In Numbers \u2013 Mathematical&nbsp;Style<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2020\/01\/02\/2020-in-numbers-mathematical-style\/\">2020 In Numbers \u2013 Mathematical Style \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Factorial-Type Numerical Calendar<\/em><\/strong>,&nbsp;\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2020\/06\/02\/factorial-type-numerical-calendar\/\">Factorial-Type Numerical Calendar \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <strong><em>21 Mathematical Highlights for 2021<\/em>&nbsp;<\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2020\/12\/28\/21-mathematical-hightlights-for-2021\/\">21 Mathematical Hightlights for 2021 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2021\/01\/02\/more-on-2021\/\">More on 2021 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em><strong>Geometrical, Numerical, and Symmetrical Representations for the Days of 2020<\/strong><\/em>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2020\/10\/07\/geometrical-numerical-and-symmetrical-representations-for-the-days-of-2020\/\">Geometrical, Numerical, and Symmetrical Representations for the Days of 2020 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Hardy-Ramanujan Number \u2013 1729<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2021\/12\/25\/hardy-ramanujan-number-1729-revised\/\">Hardy-Ramanujan Number \u2013 1729: Revised \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=149\">Hardy-Ramanujan Number \u2013 1729 \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 1 and Part 2.<\/em>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/numbers-magic.com\/?p=149\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 1 \u2013 Recreating Numbers<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=13751\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 2 \u2013 Magic Squares<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <strong><em>Mathematical Beauty of 2022<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2021\/12\/27\/mathematical-beauty-of-2022\/\">Mathematical Beauty of 2022 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=319\">Mathematical Beauty of 2022 \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>23 and 2023 in Numbers and Patterns<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2023\/01\/01\/23-and-2023-in-numbers-and-patterns\/\">23 and 2023 in Numbers and Patterns \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=7264\">23 and 2023 in Numbers and Patterns \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Last Day of the Year 23 Written American Style: 12.31.23 (123123)<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/numbers-magic.com\/?p=11234\">Last Day of the Year 23 Written American Style: 12.31.23 (123123) \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Mathematical Aspects of 24 and 2024<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/numbers-magic.com\/?p=11269\">Mathematical Aspects of 24 and 2024 \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <strong><em>Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li>Part 1:&nbsp;<a href=\"https:\/\/numbers-magic.com\/wp-admin\/post.php?post=13841\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=13652\">Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares \u2013 Part 1<\/a>&nbsp;(new site)&nbsp;or<br>Part 1:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/12\/24\/reflexive-year-25-mathematics-of-25-and-2025-in-numbers-and-magic-squares-part-1\/\">Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares \u2013 Part 1<\/a>&nbsp;(old site)<\/li>\n\n\n\n<li>Part 2:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=13841\">Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares \u2013 Part 2<\/a>&nbsp;(new site) or<br>Part 2:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/12\/24\/reflexive-year-25-mathematics-of-25-and-2025-in-numbers-and-magic-squares-part-2\/\"><\/a><a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/12\/24\/reflexive-year-25-mathematics-of-25-and-2025-in-numbers-and-magic-squares-part-2\/\">Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares \u2013 Part 2<\/a>&nbsp;(old site)<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">2. Work on S. Ramanujan and Hardy-Ramanujan Number 1729<\/mark><\/h3>\n\n\n\n<p><\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 53%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Hardy-Ramanujan Number \u2013 1729, Zenodo, December 22, 2021, <strong>Zenodo<\/strong>, pp. 1-106, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.5799640.\">https:\/\/doi.org\/10.5281\/zenodo.5799640.<\/a>\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2017\/07\/29\/hardy-ramanujan-number-1729-july-29-17\/\">Hardy-Ramanujan Number \u2013 1729 \u2013 July 29, 17 \u2013 Numbers Magic<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729, <strong>Zenodo<\/strong>, December 20, 2024, pp. 1-127, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14538297\">https:\/\/doi.org\/10.5281\/zenodo.14538297<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link1: Part 1:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2021\/12\/25\/hardy-ramanujan-number-1729-revised\/\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 1<\/a>&nbsp;(old site)<br>Site Link1: Part 1:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=149\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 1<\/a>&nbsp;(new site)<\/li>\n\n\n\n<li>Site Link2: Part 2:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/12\/24\/numbers-and-magic-squares-representations-of-hardy-ramanujan-number-1729-part-2\/\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 2&nbsp;<\/a>(old site)<br>Site Link2: Part 2:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=13751\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 2<\/a>&nbsp;(new site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, 207 Magic Squares in Honor of the 138th Anniversary of S. Ramanujan with Hardy-Ramanujan Number 1729, Zenodo, December 27, 2025, pp. 1-77, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.18064853\">https:\/\/doi.org\/10.5281\/zenodo.18064853<\/a>\n<ul class=\"wp-block-list\">\n<li>Site Link1: <a href=\"https:\/\/numbers-magic.com\/?p=17312\">207 Magic Squares in Honor of the 138th Anniversary of S. Ramanujan with Hardy-Ramanujan Number 1729<\/a> (new site)<\/li>\n\n\n\n<li>Site Link2: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/12\/22\/153-magic-squares-in-honor-of-the-138th-anniversary-of-s-ramanujan-with-magic-sum-1729\/\">207Magic Squares in Honor of the 138th Anniversary of S. Ramanujan with Hardy-Ramanujan Number 1729 <\/a>(old site)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\">3<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">. Crazy Representations: Increasing and Decreasing Orders<\/mark><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Numbers from 0 to 300.000<\/mark><\/h4>\n\n\n\n<ol class=\"wp-block-list has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9<\/em>, Jan. 2014, pp.1-161,&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1302.1479\">http:\/\/arxiv.org\/abs\/1302.1479<\/a>. <\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers From 11112 to 20000<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 18, 2019, pp. 1-224,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2543626\">http:\/\/doi.org\/10.5281\/zenodo.2543626<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers From 20001 to 40000<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 03, 2021, pp. 1-541,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5642776\">https:\/\/doi.org\/10.5281\/zenodo.5642776<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers From 40001 to 60000<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 03, 2021, pp. 1-541,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5642826\">https:\/\/doi.org\/10.5281\/zenodo.5642826<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers From 60001 to 80000<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 03, 2021, pp. 1-537,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5642896\">https:\/\/doi.org\/10.5281\/zenodo.5642896<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,<em> Crazy Representations of Natural Numbers From 80001 to 100000<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 03, 2021, pp. 1-533,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5642929\">https:\/\/doi.org\/10.5281\/zenodo.5642929<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 100001 to 120000<\/em> <em>&#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 02, 2024, pp. 1-527, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13152357\">https:\/\/doi.org\/10.5281\/zenodo.13152357<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 120001 to 140000- Revised<\/em>, <strong>Zenodo<\/strong>, August 02, 2024, pp. 1-524, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13153617\">https:\/\/doi.org\/10.5281\/zenodo.13153617<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 140001 to 160000 &#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 02, 2024, pp. 1-526, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13153790\">https:\/\/doi.org\/10.5281\/zenodo.13153790<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 160000 to 180000 &#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 02, 2024, pp. 1-521, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13153929\">https:\/\/doi.org\/10.5281\/zenodo.13153929<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 180000 to 200000 &#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 02, 2024, pp. 1-526, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13154022\">https:\/\/doi.org\/10.5281\/zenodo.13154022<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 200001 to 220000 &#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 05, 2024, pp. 1-526, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13215779\">https:\/\/doi.org\/10.5281\/zenodo.13215779<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 220001 to 240000 &#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 05, 2024, pp. 1-531, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13215838\">https:\/\/doi.org\/10.5281\/zenodo.13215838<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 240001 to 260000 &#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 05, 2024, pp. 1-529, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13215887\">https:\/\/doi.org\/10.5281\/zenodo.13215887<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 260001 to 280000 &#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 05, 2024, pp. 1-534,<a href=\" https:\/\/doi.org\/10.5281\/zenodo.13215912\"> https:\/\/doi.org\/10.5281\/zenodo.13215912<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Representations of Natural Numbers from 280001 to 300000 &#8211; Revised<\/em>, <strong>Zenodo<\/strong>, August 05, 2024, pp. 1-532, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13215947\">https:\/\/doi.org\/10.5281\/zenodo.13215947<\/a>.<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Non-Sequential Numbers Representations<\/mark><\/h4>\n\n\n\n<ol class=\"wp-block-list has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 02, 2022, pp. 1-238,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5813778\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.5813778<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 06, 2022, pp. 1-266,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5826240\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.5826240<\/a>.<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Different Types Representations<\/mark><\/h4>\n\n\n\n<ol class=\"wp-block-list has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Crazy Representations of Natural Numbers 0 to 10000 Using Triangular Numbers, <strong>Zenodo<\/strong>, pp. 1-259, 2024, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10516039\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.10516039<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Crazy Representations of Natural Numbers from 0 to 10000 Using Fibonacci Sequence Values, <strong>Zenodo<\/strong>, pp. 1-261, 2024, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10501468\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.10501468<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Crazy Representations of Natural Numbers from 0 to 10000 Using Square Function, <strong>Zenodo<\/strong>, March 28, 2024, pp. 1- 259, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10892480\">https:\/\/doi.org\/10.5281\/zenodo.10892480<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Crazy Representations of Natural Numbers from 0 to 10000 Using Cubic Function, <strong>Zenodo<\/strong>, March 30, 2024, pp. 1-259, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10899695\">https:\/\/doi.org\/10.5281\/zenodo.10899695<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Natural Numbers From 1 to 20000 in Terms of Fibonacci Sequence and Triangular Numbers<\/em>.&nbsp;<strong>Zenodo<\/strong>, February 3, 2019, pp. 1-491,&nbsp; <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2575093\">http:\/\/doi.org\/10.5281\/zenodo.2575093<\/a>.<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,245,203) 0%,rgb(174,196,79) 12%,rgb(182,227,212) 50%,rgb(255,255,255) 65%,rgb(51,167,181) 100%)\">Site Links of Crazy Representations<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\n<li><strong>Inder J. Taneja, <\/strong><em><strong>The Crazy Representations and 10958 Problem<\/strong><\/em>&nbsp;\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2018\/11\/16\/crazy-representations-of-natural-numbers-the-10958-problem\/\">Crazy Representations of Natural Numbers \u2013 The 10958 Problem \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=893\">Crazy Representations of Natural Numbers \u2013 The 10958 Problem \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Crazy Representations of Natural Numbers Using Factorial: From 20001-100000<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2021\/12\/07\/crazy-representations-of-natural-numbers-using-factorial-from-20-001-100-000\/\">Crazy Representations of Natural Numbers Using Factorial: From 20001-100000 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=12194\">Crazy Representations of Natural Numbers Using Factorial: From 20001-100000 \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Crazy Representations of Natural Numbers Using Factorial: From 100001-200000<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2021\/12\/11\/crazy-representations-of-natural-numbers-using-factorial-from-100001-200000\/\">Crazy Representations of Natural Numbers Using Factorial: From 100001-200000 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=311\">Crazy Representations of Natural Numbers Using Factorial: From 100001-200000 \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2022\/01\/09\/crazy-representations-of-natural-numbers-using-factorial-from-200001-to-300000\/\">Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=459\">Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2022\/01\/06\/representation-of-numbers-from-1-to-20000-in-terms-of-palindromic-digits-1357-9-7531\/\">Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=449\">Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531 \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202,&nbsp;<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2022\/01\/02\/representation-of-numbers-from-1-to-10000-in-terms-of-palindromic-digits-2022-2202\/\">Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202 \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <em>Multiple Choices for Crazy Representations of Natural Numbers<\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/08\/06\/multiple-choices-for-crazy-representations-of-natural-numbers\/\">Multiple Choices for Crazy Representations of Natural Numbers \u2013 Numbers Magic (wordpress.com)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/numbers-magic.com\/?p=11640\">Multiple Choices for Crazy Representations of Natural Numbers \u2013 Recreating Numbers and Magic Squares (numbers-magic.com)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\">4<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">. Permutable Bases and Powers Representations<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Power Representations of Natural Numbers<\/em>, RGMIA Research Report Collection, <strong>19<\/strong>(2016), Art. 31, pp.1-71, <a href=\"http:\/\/rgmia.org\/papers\/v19\/v19a31.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/rgmia.org\/papers\/v19\/v19a31.pdf<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Flexible Power Representations of Natural Numbers<\/em>, RGMIA Research Report Collection,<strong>19<\/strong>(2016), Art 131, pp. 1-91, <a href=\"http:\/\/rgmia.org\/papers\/v19\/v19a131.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/rgmia.org\/papers\/v19\/v19a131.pdf<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Pyramidical Representations of Natural Numbers<\/em>, RGMIA Research Report Collection,&nbsp;<strong>19<\/strong>(2016), pp.1-95, Art 58,&nbsp;<a href=\"http:\/\/rgmia.org\/papers\/v19\/v19a58.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/rgmia.org\/papers\/v19\/v19a58.pdf<\/a><strong>.<\/strong>&nbsp;<br>Site link: <em>Pyramidical-Type Representations of Natural Numbers<\/em>, <a href=\"https:\/\/inderjtaneja.com\/2017\/08\/20\/pyramidical-type-representations-of-natural-numbers\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/inderjtaneja.wordpress.com\/2017\/08\/20\/pyramidical-type-representations-of-natural-numbers<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>All Digits Flexible Power Representations of Natural Numbers From 11112 to 30000<\/em>, Zenodo, January 14, 2019, pp. 1-140, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2539203\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2539203<\/a>. <\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>All Digits Flexible Power Representations of Natural Numbers From 30001 to 50000<\/em>, <strong>Zenodo<\/strong> , January 14, 2019, pp. 1-147, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2539412\">http:\/\/doi.org\/10.5281\/zenodo.2539412<\/a>. <br>Site link: <em>Flexible Power Representations: Equal String Lengths<\/em>, <a href=\"https:\/\/inderjtaneja.com\/2017\/08\/20\/flexible-power-representations-equal-string-lengths\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/inderjtanejawordpress.com\/2017\/08\/20\/flexible-power-representations-equal-string-lengths<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Permutable Power Minimum Length Representations of Natural Numbers from 0 to 20000<\/em>, <strong>Zenodo<\/strong>, January, 30, 2019, pp. 1-288, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2553326\">http:\/\/doi.org\/10.5281\/zenodo.2553326<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Pyramid-Type Representations of Natural Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 5, 2020, pp.&nbsp;1-213,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.3637662\">http:\/\/doi.org\/10.5281\/zenodo.3637662<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Pyramid-Type Representations of Natural Numbers from 1001 to 10000<\/em>, <strong>Zenodo<\/strong>, January 16, 2024, pp. 1-585, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.10520278\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.10520278<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">5. Running Expressions: Sequential Representations<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Running Expressions in Increasing and Decreasing Orders of Natural Numbers Separated by Equality Signs<\/em>, RGMIA Research Report Collection,&nbsp;<strong>18<\/strong>(2015), Article 27, pp.1-54, <a href=\"http:\/\/rgmia.org\/papers\/v18\/v18a27.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/rgmia.org\/papers\/v18\/v18a27.pdf<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Running Expressions with Equalities: Increasing and Decreasing Orders \u2013 I<\/em>, RGMIA Research Report Collection,&nbsp;<strong>20<\/strong>(2017), Art. 33, pp.1-57,&nbsp;<a href=\"http:\/\/rgmia.org\/papers\/v20\/v20a33.pdf\">http:\/\/rgmia.org\/papers\/v20\/v20a33.pdf<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Running Expressions with Equalities: Increasing and Decreasing Orders \u2013 II<\/em>, RGMIA Research Report Collection,&nbsp;<strong>20<\/strong>(2017), Art. 34, pp.1-87,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/rgmia.org\/papers\/v20\/v20a34.pdf\" target=\"_blank\">http:\/\/rgmia.org\/papers\/v20\/v20a34.pdf<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Fibonacci Sequence and Running Expressions with Equalities \u2013 I<\/em>, RGMIA Research Report Collection,&nbsp;<strong>20<\/strong>(2017), Art. 35, pp. 1-83,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/rgmia.org\/papers\/v20\/v20a35.pdf\" target=\"_blank\">http:\/\/rgmia.org\/papers\/v20\/v20a35.pdf<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Running Expressions with Triangular Numbers \u2013 I<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 21, 2018,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2483327\">http:\/\/doi.org\/10.5281\/zenodo.2483327<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Crazy Running Equality Expressions with Factorial and Square-Root<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 06, 2021, pp. 1-464,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5761752\">https:\/\/doi.org\/10.5281\/zenodo.5761752<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\">6<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">. Single Digit and Letter Representations<\/mark><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Single Digit<\/mark><\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Single Digit Representations of Natural Numbers<\/em>, Feb. 1015, pp.1-55, <a rel=\"noreferrer noopener\" href=\"http:\/\/arxiv.org\/abs\/1502.03501\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1502.03501<\/a>. <br>Site link: <em>Single Digits Representations of Numbers from 1 to 20000<\/em>, <a href=\"https:\/\/inderjtaneja.com\/2019\/01\/01\/single-letter-representations-of-numbers-from-1-to-20000\">https:\/\/inderjtaneja.com\/2019\/01\/01\/single-letter-representations-of-numbers-from-1-to-20000<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Digit Representations of Natural Numbers From 1 to 5000,<\/em>&nbsp;<strong>Zenodo<\/strong>, January 14, 2019,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2538893\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2538893<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Digit Representations of Natural Numbers From 5001 to 10000<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 14, 2019,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2538897\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2538897<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Digit Representations of Numbers From 10001 to 15000<\/em>,&nbsp;<strong>Zenodo<\/strong>, January, 26, 2019, pp. 1-510,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2550414\">http:\/\/doi.org\/10.5281\/zenodo.2550414<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Digit Representations of Numbers From 15001 to 20000<\/em>,<strong>&nbsp;Zenodo<\/strong>, January, 26, 2019, pp. 1-510,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2550440\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2550440<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterned Single Digits Representations of Natural Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 04, 2020, pp. 1-590,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3930382\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3930382<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Single Digit Representations of Natural Numbers From 20001 to 30000<\/em>, <strong>Zenodo<\/strong>, March 21, 2022, pp. 1-1271, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.6373774\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.6373774<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Single Digit Representations of Natural Numbers From 30001 to 40000<\/em>, <strong>Zenodo<\/strong>, March 23, 2022, pp. 1-1269, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.6379827\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.6379827<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Single Digit Representations of Natural Numbers From 40001 to 50000<\/em>, Zenodo, March 23, 2022, pp. 1-1268, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.6379875\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.6379875<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Patterns in Single-Digit Representations of Natural Numbers<\/em>, <strong>Zenodo<\/strong>, January 19, 2026, pp. 1-284, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.18296290\">https:\/\/doi.org\/10.5281\/zenodo.18296290<\/a><\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\"><strong>Single Letter<\/strong><\/mark><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,<em>&nbsp;Fraction-Type Single Letter Representations of Natural Numbers From 1 to 11111<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 4, 2019, pp. 1-203,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2556902\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2556902<\/a>. <br>Site link: <em>Single Letter Representations of Natural Numbers<\/em>, <a rel=\"noreferrer noopener\" href=\"https:\/\/inderjtaneja.com\/2017\/08\/19\/single-letter-representations-of-natural-numbers\" target=\"_blank\">https:\/\/inderjtaneja.com\/2017\/08\/19\/single-letter-representations-of-natural-numbers<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Letter Representations of Natural Numbers from 1 to 11111<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 5, 2019, pp. 1-133,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2557025\">http:\/\/doi.org\/10.5281\/zenodo.2557025<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Letter Patterned Representations and Fibonacci Sequence Values<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 6, 2019, pp. 1-40,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2558522\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2558522<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Patterned Single Letter Representations of Natural Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 02, 2020, pp. 1-110,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3928507\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3928507<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\">7<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">. Narcissistic-Type<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Flexible Powers Narcissistic-Type Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 19, 2019, pp. 1-126, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2572770\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2572770<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fixed and Flexible Powers Narcissistic Numbers with Division<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 19, 2019, pp. 1-142,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2573047\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2573047<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fixed and Flexible Powers Narcissistic Numbers with Division<\/em>&nbsp;(revised),&nbsp;<strong>Zenodo<\/strong>, May 11, 2020, pp. 1-201,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.3820428\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3820428<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Unified Study of Narcissistic Numbers without and with Division, \\textbf{Zenodo}, Feb. 15, 2024, pp. 1-353, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.10662872\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.10662872<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\">8<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">. Selfie Expressions<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Same Digits Equalities Expressions,&nbsp;<\/em><strong>Zenodo<\/strong>,&nbsp;February 19, 2019, pp. 1-182, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2573194\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2573194<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Factorial-Power Selfie Expressions<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 20, 2019, pp. 1-115, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2573569\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2573569<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Selfie Expressions with Factorial, Fibonacci and Triangular Values<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 20, 2019, pp. 1-180,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2574151\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2574151<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Same Digits Equality Expressions: Power and Plus,&nbsp;<strong>Zenodo<\/strong>, January 03, 2020, 2019, pp. 1-1729,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3597506\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3597506<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\">9<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">. Selfie Numbers<\/mark><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Permutable, Basic Operations, Factorial and Square-Root<\/mark><\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Permutable Powers Selfie Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 15, 2019, pp. 1-227, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2566445\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2566445<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Selfie Numbers: Basic Operations<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 26, 2019, pp. 1-134, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2609143\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2609143<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Factorial-Type Selfie Numbers in Digit\u2019s Order<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 06, 2019, pp. 1-243, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2585586\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2585586<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Factorial-Type Selfie Numbers in Reverse Order of Digits<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 06, 2019, pp. 1-227,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2585599\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2585599<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Square-Root Type Selfie Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 06, 2019, pp. 1-248, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3352388\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3352388<\/a>.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Fibonacci and Triangular Numbers<\/mark><\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fibonacci Sequence and Selfie Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 19, 2019, pp. 1-233, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2572044\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2572044<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Triangular-Type Selfie Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 17, 2019, pp. 1-91 &nbsp;&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2567571\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2567571<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Simultaneous Representations of Selfie Numbers in Terms of Fibonacci and Triangular Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 19, 2019, pp. 1-233,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2574136\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2574136<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Triangular-Type Selfie Numbers: Digit\u2019s Order,<\/em>&nbsp;<strong>Zenodo<\/strong>, April 11, 2019, pp. 1-240, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2636787\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2636787<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Triangular-Type Selfie Numbers: Reverse Order of Digits,&nbsp;<\/em><strong>Zenodo<\/strong>, April 14, 2019, pp. 1-249, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2639099\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2639099<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fibonacci Sequence Type Selfie Numbers: Basic Operations,<\/em><strong>&nbsp; Zenodo<\/strong>, April 28, 2019, pp. 1-163,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2653093\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2653093<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fibonacci Sequence Type Selfie Numbers with Square-Root<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 10, 2019, pp. 1-206,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3479255\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3479255<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fibonacci Sequence Type Selfie Numbers with Factorial: Digit\u2019s Order<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 13, 2019, pp. 1-692,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3484117\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3484117<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fibonacci Sequence Type Selfie Numbers with Factorial: Reverse Order of Digits<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 13, 2019, pp. 1-742,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3484119\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3484119<\/a>.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Binomial Coefficients<\/mark><\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Selfie Numbers with Binomial Coefficients<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 17, 2019, pp. 1-131, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2596421\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2596421<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Selfie Numbers with Binomial Coefficients and Fibonacci Numbers<\/em>.&nbsp;<strong>Zenodo<\/strong>, March 30, 2019, pp. 1-148, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2617290\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2617290<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Binomial Coefficients Triangular Type Selfie Numbers: Basic Operations<\/em>,&nbsp;<strong>Zenodo<\/strong>, April 25, 2019, pp. 1-72,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2650508\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2650508<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Selfie Numbers with Binomial Coefficients, Triangular Numbers and Square-Root<\/em>,&nbsp; <strong>Zenodo<\/strong>, May 10, 2019, pp. 1-209,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2707318\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2707318<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Selfie Numbers with Binomial Coefficients, Triangular Numbers and Factorial<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 09, 2019, pp. 1-172,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.3273300\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3273300<\/a>.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Quadratic and Cubic<\/mark><\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Quadratic-Type Selfie Numbers<\/em>, Zenodo, February 25, 2019, pp. 1-315, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2577472\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2577472<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Cubic-Type Selfie Numbers,&nbsp;<strong>Zenodo<\/strong>, March 12, 2019, pp. 1-150, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2591257\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2591257<\/a>.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Concatenation-Type<\/mark><\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Concatenation-Type Selfie Numbers with Factorial and Square-Root<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 08, 2019, pp. 1-43,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2587751\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2587751<\/a>.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Multiple Representations<\/mark><\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Multiple Representations of Selfie Numbers &#8211; I<\/em>, <strong>Zenodo<\/strong>, February 08, 2024, pp. 1-108, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10633471\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.10633471<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Multiple Representations of Selfie Numbers &#8211; II<\/em>,  <strong>Zenodo<\/strong>, April 15, 2024, pp. 1-284, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10974798\">https:\/\/doi.org\/10.5281\/zenodo.10974798<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Multiple Choice Patterns in Selfie Numbers &#8211; I<\/em>, <strong>Zenodo<\/strong>, 2024, April 15, pp. 1-85, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.10972221\">http:\/\/doi.org\/10.5281\/zenodo.10972221<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\">10<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">. Semi-Selfie Numbers<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Semi-Selfie Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 12, 2019, pp. 1-394, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2562390\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2562390<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Power-Type Semi-Selfie Numbers and Patterns<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 16, 2019, pp. 1-130, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3338366\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3338366<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterns in Selfie and Semi-Selfie Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 6, 2019, pp. 1-51 <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2563202\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2563202<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">11. Selfie Fractions<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Selfie Fractions: Addable, Subtractable, Dottable and Potentiable<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 24, 2019, pp. 1-260,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2604531\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2604531<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Pandigital Equivalent Selfie Fractions<\/em>,&nbsp;<strong>Zenodo<\/strong>, April 02, 2019, pp. 1-392,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2622028\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2622028<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Repeated Digits Selfie Fractions: Two- and Three-Digits Numerators<\/em>,&nbsp;<strong>Zenodo<\/strong>, September 12, 2019, pp. 1-1091,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3406655\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3406655<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Different Digits Selfie Fractions: Two- and Three-Digits Numerators<\/em>,&nbsp;<strong>Zenodo<\/strong>, September 12, 2019, pp. 1-337, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.3474091\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3474091<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Different Digits Selfie Fractions: Four Digits Numerator<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 06, 2019, pp. 1-844,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3474267\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3474267<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterned Selfie Fractions<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 27, 2019, pp. 1-267, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3520096\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3520096<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Different Digits Selfie Fractions: Five Digits Numerator \u2013 Pandigital<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 06, 2019, pp. 1-362,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3474379\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3474379<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Patterns in Splitted Selfie Fractions, <strong>Zenodo<\/strong>, July 30, 2023, pp. 1-122, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.8197701\">http:\/\/doi.org\/10.5281\/zenodo.8197701<\/a><\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">12. Equivalent Fractions<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Different Digits Equivalent Fractions \u2013 I<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 24, 2019, pp. 1-165, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2604565\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2604565<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Different Digits Equivalent Fractions \u2013 II<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 24, 2019, pp. 1-244, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2604738\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2604738<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Different Digits Equivalent Fractions: Single Digit Numerator<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 15, 2019, pp. 1-794,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3543532\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3543532<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Different Digits Equivalent Fractions: Two Digits Numerator<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 15, 2019, pp. 1-794,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3543752\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3543752<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Different Digits Equivalent Fractions: Three Digits Numerator<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 19, 2019, pp. 1-1014,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3547874\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3547874<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">13. Amicable Numbers<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Amicable Numbers with Patterns in Products and Powers<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 05, 2019, pp. 1-25,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2583306\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2583306<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">14. <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Palindromic-Type Representations<\/mark><\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Palindromic-Type Palindromes \u2013 I<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 15, 2019, pp. 1-99 <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2541174\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2541174<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Palindromic-Type Non-Palindromes \u2013 I<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 15, 2019, pp. 1-117, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2541187\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2541187<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Palindromic-Type Squared Expressions with Palindromic and Non-Palindromic Sums \u2013 I<\/em>,&nbsp; <strong>Zenodo<\/strong>, January 15, 2019, pp. 1-133,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2541198\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2541198<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">15. Pythagorean Triples<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterns in Pythagorean Triples Using Single and Double Variable Procedures<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 19, 2019, pp. 1-134,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2544519\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2544519<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Multiple-Type Patterns and Pythagorean Triples<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 19, 2019, pp.1-53, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2544527\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2544527<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Palindromic-Type Pandigital Patterns in Pythagorean Triples<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 20, 2019, pp. 1-160,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2544551\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2544551<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Generating Pythagorean Triples, Patterns, and Magic Squares<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 20, 2019, pp. 1-121,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2544555\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2544555<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Patterns in Pythagorean Triples,&nbsp;<strong>Zenodo<\/strong>, March 13, 1-136, 2021,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.4603197\">http:\/\/doi.org\/10.5281\/zenodo.4603197<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Pandigital-Type and Pythagorean Triples Patterns,&nbsp;<strong>Zenodo<\/strong>, March 17, 1-750, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.4611511\">http:\/\/doi.org\/10.5281\/zenodo.4611511<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">16. Prime Numbers<\/mark><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Fixed Digits Repetitions<\/mark><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fixed Digits Repetitions Prime Patterns of Lengths 10, 9 and 8,&nbsp;<\/em><strong>Zenodo<\/strong>, February 8, 2019, pp. 1-175,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2560640\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2560640<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fixed Digits Repetitions Prime Patterns of Length 7<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 8, 2019, pp. 1-176,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2560668\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2560668<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Fixed Digits Repetitions Prime Patterns of Length 6<\/em>.&nbsp;<strong>Zenodo<\/strong>, February 9, 2019, pp. 1-303,<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2561096\" target=\"_blank\">&nbsp;http:\/\/doi.org\/10.5281\/zenodo.2561096<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Prime Numbers in Fixed Digits Repetitions Prime Patterns<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 10, 2020, pp. 1-280,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.4265818\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.4265818<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>4-Digits Prime Numbers in Fixed Digits Repetition Prime Patterns<\/em>,&nbsp;<strong>Zenodo<\/strong>, November 29, 2020, pp. 1-1544,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.4295652\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.4295652<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Fixed Digits Repetitions Prime Patterns for 5-Digits Prime Numbers,<strong>&nbsp;Zenodo<\/strong>, January 17, 2021, pp. 1-2069,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.4445395\">http:\/\/doi.org\/10.5281\/zenodo.4445395<\/a>.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Magic Square Type Palindromic Primes<\/mark><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, Magic Squares Type Palprimes of Orders 5\u00d75, 7\u00d77 and 9\u00d79,&nbsp;<strong>Zenodo<\/strong>, February 27, 2019, pp. 1-143,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2578443\">http:\/\/doi.org\/10.5281\/zenodo.2578443<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Same Digits Embedded Palprimes of Lengths 3, 5 and 7<\/em>,&nbsp;<strong>Zenodo<\/strong>, August 08, 2020, pp. 1-315,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3977028\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3977028<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>3 and 5-Digits Multiple Choice Embedded Palprimes<\/em>,&nbsp;<strong>Zenodo<\/strong>, December 05, 2020, pp. 1-511,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.4307875\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.4307875<\/a>.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Prime Numbers in Prime Numbers<\/mark><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Prime Numbers in Prime Numbers Up To 5 Digits<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 16, 2019, pp. 1-265,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.3338679\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.3338679<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">17. Power Expressions<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Multiple Choice Power Expressions<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 15, 2019, pp. 1-143,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2565729\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2565729<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-left has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(67,115,204,0.07) 81%,rgb(255,105,0) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">18. Patterns in Numbers<\/mark><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Amicable Numbers with Patterns in Products and Powers<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 05, 2019, pp. 1-25,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2583306\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2583306<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterned Selfie Fractions<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 27, 2019, pp. 1-267, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.3520096\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3520096<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterns in Selfie and Semi-Selfie Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 6, 2019, pp. 1-51 <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2563202\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2563202<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Single Letter Patterned Representations and Fibonacci Sequence Values<\/em>, Zenodo, Feb 06, 2019, 1-40,  <a href=\"https:\/\/doi.org\/10.5281\/zenodo.2558522\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.2558522<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterned Single Digits Representations of Natural Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 04, 2020, pp. 1-590,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.3930382\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3930382<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Patterned Single Letter Representations of Natural Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 02, 2020, pp. 1-110,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.3928507\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3928507<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterned Selfie Fractions<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 27, 2019, pp. 1-267, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.3520096\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3520096<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Patterns in Splitted Selfie Fractions<\/em>, <strong>Zenodo<\/strong>, July 30, 2023, pp. 1-122, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.8197701\">http:\/\/doi.org\/10.5281\/zenodo.8197701<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Patterns in Selfie Numbers &#8211; I<\/em>, <strong>Zenodo<\/strong>, 2024, February 10, pp. 1-26, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10674570\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.10674570<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterns in Pythagorean Triples Using Single and Double Variable Procedures<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 19, 2019, pp. 1-134,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2544519\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2544519<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Multiple-Type Patterns and Pythagorean Triples<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 19, 2019, pp.1-53, <a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2544527\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2544527<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Palindromic-Type Pandigital Patterns in Pythagorean Triples<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 20, 2019, pp. 1-160,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2544551\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2544551<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Generating Pythagorean Triples, Patterns, and Magic Squares<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 20, 2019, pp. 1-121,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/doi.org\/10.5281\/zenodo.2544555\" target=\"_blank\">http:\/\/doi.org\/10.5281\/zenodo.2544555<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Patterns in Pythagorean Triples,&nbsp;<strong>Zenodo<\/strong>, March 13, 1-136, 2021,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.4603197\">http:\/\/doi.org\/10.5281\/zenodo.4603197<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Pandigital-Type and Pythagorean Triples Patterns<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 17, 1-750, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.4611511\">http:\/\/doi.org\/10.5281\/zenodo.4611511<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Inder J. Taneja}, <em>Multiple Choice Patterns in Selfie Numbers &#8211; I<\/em>, <strong>Zenodo<\/strong>, 2024, April 15, pp. 1-85, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.10972221\">http:\/\/doi.org\/10.5281\/zenodo.10972221<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Patterned Single Letter Representations of Natural Numbers<\/em>, <strong>Zenodo<\/strong>, July 02, 2020, pp. 1-110, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.3928507\">http:\/\/doi.org\/10.5281\/zenodo.3928507<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Patterns in Single-Digit Representations of Natural Numbers<\/em>, <strong>Zenodo<\/strong>, January 19, 2026, pp. 1-284, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.18296290\">https:\/\/doi.org\/10.5281\/zenodo.18296290<\/a><\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-justify\"><em>All the work given in this part of <strong>&#8220;patterns in numbers&#8221;<\/strong> is repeated from other works given in previous parts. These are written here to give importance to <strong>pattened work on numbers<\/strong>.<\/em><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. General Work Site Links of General Work 2. Work on S. Ramanujan and Hardy-Ramanujan Number 1729 3. Crazy Representations: Increasing and Decreasing Orders Numbers from 0 to 300.000 Non-Sequential Numbers Representations Different Types Representations Site Links of Crazy Representations 4. Permutable Bases and Powers Representations 5. Running Expressions: Sequential Representations 6. Single Digit and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[13],"tags":[],"class_list":["post-671","post","type-post","status-publish","format-standard","hentry","category-publi-ca-tions"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/671","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=671"}],"version-history":[{"count":39,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/671\/revisions"}],"predecessor-version":[{"id":17740,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/671\/revisions\/17740"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}