{"id":17940,"date":"2026-02-08T23:18:57","date_gmt":"2026-02-09T02:18:57","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=17940"},"modified":"2026-02-08T23:19:01","modified_gmt":"2026-02-09T02:19:01","slug":"38th-39th-and-40th-days-of-the-year-07-08-26-08-02-26-and-09-02-26-recreating-numbers-and-patterns","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=17940","title":{"rendered":"38th, 39th and 40th Days of the Year: 07.08.26, 08.02.26 and 09.02.26 \u2013 Recreating Numbers and Patterns"},"content":{"rendered":"<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1320\" height=\"1437\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/02\/d-38-40-0226.png\" alt=\"\" class=\"wp-image-17941\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/02\/d-38-40-0226.png 1320w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/02\/d-38-40-0226-276x300.png 276w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/02\/d-38-40-0226-941x1024.png 941w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/02\/d-38-40-0226-768x836.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/02\/d-38-40-0226-535x582.png 535w\" sizes=\"(max-width: 1320px) 100vw, 1320px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-blush-light-purple-gradient-background has-background\">References <\/h3>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-2110a66ceb79608d7a64df0d3ce58fd5\">1. Crazy Representations<\/h3>\n\n\n\n<ol class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\n<li><strong>Inder J. Taneja,&nbsp;<\/strong><em><strong>The Crazy Representations and 10958 Problem<\/strong><\/em>\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,&nbsp;<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,&nbsp;<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,&nbsp;<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,&nbsp;<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,&nbsp;<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,&nbsp;<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<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-734d1aa23134df0de6cdb2676273bbba\">2. Running Equalitiy Expressions<\/h3>\n\n\n\n<ol class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<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>,&nbsp;<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, <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>,&nbsp;<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 href=\"http:\/\/rgmia.org\/papers\/v20\/v20a34.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/rgmia.org\/papers\/v20\/v20a34.pdf<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<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 href=\"http:\/\/rgmia.org\/papers\/v20\/v20a35.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/rgmia.org\/papers\/v20\/v20a35.pdf<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<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>,&nbsp;<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<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-e1726d59a4cd18023691950b0079ec67\">2. Single-Digit Representations and Patterns<\/h3>\n\n\n\n<ol class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Digit Representations of Natural Numbers<\/em>, Feb. 1015, pp.1-55,&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1502.03501\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/arxiv.org\/abs\/1502.03501<\/a>.<br>Site link:&nbsp;<em>Single Digits Representations of Numbers from 1 to 20000<\/em>,&nbsp;<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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2538893\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2538897\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2550440\" target=\"_blank\" rel=\"noreferrer noopener\">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 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>,&nbsp;<em>Single Digit Representations of Natural Numbers From 20001 to 30000<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 21, 2022, pp. 1-1271,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.6373774\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.6373774<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Digit Representations of Natural Numbers From 30001 to 40000<\/em>,&nbsp;<strong>Zenodo<\/strong>, March 23, 2022, pp. 1-1269,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.6379827\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.6379827<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Single Digit Representations of Natural Numbers From 40001 to 50000<\/em>, Zenodo, March 23, 2022, pp. 1-1268,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.6379875\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.5281\/zenodo.6379875<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<em>Patterns in Single-Digit Representations of Natural Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, January 19, 2026, pp. 1-284,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.18296290\">https:\/\/doi.org\/10.5281\/zenodo.18296290<\/a>.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-ea07883b5b161d83d79e2323d715c6d9\">3. Pattern in Pythagorean Triples<\/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<\/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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2544527\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2544551\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2544555\" target=\"_blank\" rel=\"noreferrer noopener\">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, <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>,&nbsp;<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<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-1b869bf9a8819442f769fa3219d81a26\">4. Semi-Selfie Representations<\/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<\/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>,&nbsp;<em>Semi-Selfie Numbers<\/em>,&nbsp;<strong>Zenodo<\/strong>, February 12, 2019, pp. 1-394, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2562390\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.3338366\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3338366<\/a>.<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-0731bf9155d9b7b74ee510a559672784\">5. Selfie-Fractions and Patterns<\/h3>\n\n\n\n<ol class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2604531\" target=\"_blank\" rel=\"noreferrer noopener\">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, <a href=\"http:\/\/doi.org\/10.5281\/zenodo.2622028\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.3406655\" target=\"_blank\" rel=\"noreferrer noopener\">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,&nbsp;<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 href=\"http:\/\/doi.org\/10.5281\/zenodo.3474267\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3474267<\/a>.<\/li>\n\n\n\n<li><strong>nder 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>Different Digits Selfie Fractions: Five Digits Numerator \u2013 Pandigital<\/em>,&nbsp;<strong>Zenodo<\/strong>, October 06, 2019, pp. 1-362,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.3474379\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3474379<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Patterns in Splitted Selfie Fractions,&nbsp;<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-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-975290b1eeb8dea1918626945369ab29\">4. Narcissistic-Type Representations<\/h3>\n\n\n\n<ol class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\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,&nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2572770\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2573047\" target=\"_blank\" rel=\"noreferrer noopener\">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, <strong>Zenodo<\/strong>, Feb. 15, 2024, pp. 1-353,&nbsp;<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<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-fc08585c71fe44736ea596cc98d85364\">5. Fixed Digits Repetitions <\/h4>\n\n\n\n<ol class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2560640\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2560668\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.2561096\" target=\"_blank\" rel=\"noreferrer noopener\">&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 href=\"http:\/\/doi.org\/10.5281\/zenodo.4265818\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.4295652\" target=\"_blank\" rel=\"noreferrer noopener\">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<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-d3b24549adaf3c9b1c95d0b4c965b02a\">6. Embedded Prime Patterns <\/h4>\n\n\n\n<ol class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\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 href=\"http:\/\/doi.org\/10.5281\/zenodo.3977028\" target=\"_blank\" rel=\"noreferrer noopener\">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 href=\"http:\/\/doi.org\/10.5281\/zenodo.4307875\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.4307875<\/a>.<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>References 1. Crazy Representations 2. Running Equalitiy Expressions 2. Single-Digit Representations and Patterns 3. Pattern in Pythagorean Triples 4. Semi-Selfie Representations 5. Selfie-Fractions and Patterns 4. Narcissistic-Type Representations 5. Fixed Digits Repetitions 6. Embedded Prime Patterns<\/p>\n","protected":false},"author":1,"featured_media":17941,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-17940","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-days-of-year"],"jetpack_featured_media_url":"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/02\/d-38-40-0226.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/17940","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=17940"}],"version-history":[{"count":1,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/17940\/revisions"}],"predecessor-version":[{"id":17942,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/17940\/revisions\/17942"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/17941"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=17940"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=17940"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=17940"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}