{"id":12033,"date":"2024-06-11T14:31:26","date_gmt":"2024-06-11T17:31:26","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=12033"},"modified":"2024-06-11T14:31:27","modified_gmt":"2024-06-11T17:31:27","slug":"163rd-days-of-the-year-11-06-24-single-letter-and-crazy-representations","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=12033","title":{"rendered":"163rd Days of the Year: 11.06.24 &#8211; Single Letter and Crazy Representations"},"content":{"rendered":"<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"815\" height=\"1377\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/day-163.png\" alt=\"\" class=\"wp-image-12034\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/day-163.png 815w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/day-163-178x300.png 178w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/day-163-606x1024.png 606w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/day-163-768x1298.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/day-163-535x904.png 535w\" sizes=\"(max-width: 815px) 100vw, 815px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"820\" height=\"1126\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Crazy-163.png\" alt=\"\" class=\"wp-image-12035\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Crazy-163.png 820w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Crazy-163-218x300.png 218w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Crazy-163-746x1024.png 746w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Crazy-163-768x1055.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Crazy-163-535x735.png 535w\" sizes=\"(max-width: 820px) 100vw, 820px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-blush-light-purple-gradient-background has-background\">References<\/h2>\n\n\n\n<p><\/p>\n\n\n\n<ol class=\"has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<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,\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1302.1479\">http:\/\/arxiv.org\/abs\/1302.1479<\/a>.<\/li>\n\n\n\n<li><strong>Site link:<\/strong>\u00a0<em>Crazy Representations of Natural Numbers \u2013 The 10958 Problem<\/em>,\u00a0<a href=\"https:\/\/inderjtaneja.com\/2018\/11\/16\/crazy-representations-of-natural-numbers-the-10958-problem\">https:\/\/inderjtaneja.com\/2018\/11\/16\/crazy-representations-of-natural-numbers-the-10958-problem<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=11418\">Mathematical Representations for Days of the Year<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=11640\">Multiple Choices for Crazy Representations of Natural Numbers<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<a href=\"https:\/\/zenodo.org\/records\/3597506\"><\/a><a href=\"https:\/\/zenodo.org\/records\/10633471\">Multiple Representations of Selfie Numbers \u2013 I (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<em>Permutable Powers Selfie Numbers<\/em>,\u00a0<strong>Zenodo<\/strong>, February 15, 2019, pp. 1-227,\u00a0\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2566445\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2566445<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<em>Selfie Numbers: Basic Operations<\/em>,\u00a0<strong>Zenodo<\/strong>, March 26, 2019, pp. 1-134,\u00a0\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2609143\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2609143<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<em>Factorial-Type Selfie Numbers in Digit\u2019s Order<\/em>,\u00a0<strong>Zenodo<\/strong>, March 06, 2019, pp. 1-243,\u00a0\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2585586\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2585586<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<em>Factorial-Type Selfie Numbers in Reverse Order of Digits<\/em>,\u00a0<strong>Zenodo<\/strong>, March 06, 2019, pp. 1-227,\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2585599\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2585599<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<em>Square-Root Type Selfie Numbers<\/em>,\u00a0<strong>Zenodo<\/strong>, July 06, 2019, pp. 1-248,\u00a0\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.3352388\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3352388<\/a><\/li>\n\n\n\n<li>.<strong>Inder J. Taneja<\/strong>,\u00a0<a href=\"https:\/\/zenodo.org\/records\/2583306\">Amicable Numbers With Patterns in Products and Powers (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,\u00a0<\/strong><a href=\"https:\/\/zenodo.org\/records\/8197701\">Patterns in Splitted Selfie Fractions (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,\u00a0<\/strong><a href=\"https:\/\/zenodo.org\/records\/10662872\">Unified Study of Narcissistic Numbers without and with Division (zenodo.org)<\/a><strong>Inder J. Taneja,\u00a0<\/strong><a href=\"https:\/\/zenodo.org\/records\/3338366\">Power-Type Semi-Selfie Numbers and Patterns (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,\u00a0<\/strong><a href=\"https:\/\/zenodo.org\/records\/5761752\">Crazy Running Equality Expressions With Factorial and Square-Root (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,\u00a0<\/strong><a href=\"https:\/\/zenodo.org\/records\/3637662\">Pyramid-Type Representations of Natural Numbers (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,\u00a0<\/strong><a href=\"https:\/\/zenodo.org\/records\/10520278\">Pyramid-Type Representations of Natural Numbers from 1001 to 10000 (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,<\/strong><a href=\"https:\/\/zenodo.org\/records\/2573194\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><a href=\"https:\/\/zenodo.org\/records\/2573569\">Factorial-Power Selfie Expressions (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,\u00a0<\/strong><a href=\"https:\/\/zenodo.org\/records\/2574151\">Selfie Expressions With Factorial, Fibonacci and Triangular Values (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,<em>\u00a0Fraction-Type Single Letter Representations of Natural Numbers From 1 to 11111<\/em>,\u00a0<strong>Zenodo<\/strong>, February 4, 2019, pp. 1-203,\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2556902\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2556902<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link:\u00a0<em>Single Letter Representations of Natural Numbers<\/em>,\u00a0 <a href=\"https:\/\/inderjtaneja.com\/2017\/08\/19\/single-letter-representations-of-natural-numbers\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/inderjtaneja.wordpress.com\/2017\/08\/19\/single-letter-representations-of-natural-numbers<\/a>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<em>Single Letter Representations of Natural Numbers from 1 to 11111<\/em>,\u00a0<strong>Zenodo<\/strong>, February 5, 2019, pp. 1-133,\u00a0<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>,\u00a0<em>Single Letter Patterned Representations and Fibonacci Sequence Values<\/em>,\u00a0<strong>Zenodo<\/strong>, February 6, 2019, pp. 1-40,\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2558522\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.2558522<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<a href=\"https:\/\/zenodo.org\/records\/2561096\">Fixed Digits Repetitions Prime Patterns of Length 6 (zenodo.org)<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<em>Single Digit Representations of Natural Numbers<\/em>, Feb. 1015, pp.1-55, <a href=\"http:\/\/arxiv.org\/abs\/1502.03501\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/arxiv.org\/abs\/1502.03501<\/a>. \n<ul class=\"wp-block-list\">\n<li>Site link:\u00a0<em>Single Digits Representations of Numbers from 1 to 20000<\/em>,\u00a0\u00a0<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<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,\u00a0<em>Patterned Single Digits Representations of Natural Numbers<\/em>,\u00a0<strong>Zenodo<\/strong>, July 04, 2020, pp. 1-590,\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.3930382\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.3930382<\/a>.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>References<\/p>\n","protected":false},"author":1,"featured_media":12034,"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-12033","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\/2024\/06\/day-163.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/12033","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=12033"}],"version-history":[{"count":1,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/12033\/revisions"}],"predecessor-version":[{"id":12036,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/12033\/revisions\/12036"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/12034"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12033"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12033"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}