{"id":14118,"date":"2025-01-03T01:04:24","date_gmt":"2025-01-03T04:04:24","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=14118"},"modified":"2025-01-03T01:04:26","modified_gmt":"2025-01-03T04:04:26","slug":"3rd-day-of-the-year-03-01-25-multiple-representations-four-color-and-pythagorean-triples-patterns","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=14118","title":{"rendered":"3rd Day of the Year: 03.01.25 \u2013 Multiple Representations, Four Color and Pythagorean Triples Patterns"},"content":{"rendered":"<div class=\"wp-block-image is-style-default\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1034\" height=\"1451\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3a-0301.png\" alt=\"\" class=\"wp-image-14119\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3a-0301.png 1034w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3a-0301-214x300.png 214w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3a-0301-730x1024.png 730w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3a-0301-768x1078.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3a-0301-535x751.png 535w\" sizes=\"(max-width: 1034px) 100vw, 1034px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image is-style-default\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"1203\" height=\"1564\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3b-0301.png\" alt=\"\" class=\"wp-image-14120\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3b-0301.png 1203w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3b-0301-231x300.png 231w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3b-0301-788x1024.png 788w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3b-0301-768x998.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3b-0301-535x696.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/Day-3b-0301-1181x1536.png 1181w\" sizes=\"(max-width: 1203px) 100vw, 1203px\" \/><\/figure>\n<\/div>\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=\"wp-block-list has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<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>.\n<ul class=\"wp-block-list\">\n<li><strong>Site link:<\/strong>&nbsp;<em>Crazy Representations of Natural Numbers \u2013 The 10958 Problem<\/em>,&nbsp; <a href=\"https:\/\/inderjtaneja.com\/2018\/11\/16\/crazy-representations-of-natural-numbers-the-10958-problem\">https:\/\/inderjtaneja.wordpress.com\/2018\/11\/16\/crazy-representations-of-natural-numbers-the-10958-problem<\/a>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<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>,&nbsp;<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>,&nbsp;<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>,&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\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,&nbsp;<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>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;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2019\/01\/01\/single-letter-representations-of-numbers-from-1-to-20000\/\">Single Digits 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>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>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>Crazy Running Equality Expressions with Factorial and Square-Root<\/em>, <strong>Zenodo<\/strong>, December 06, 2021, pp. 1-464, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.5761752\">https:\/\/doi.org\/10.5281\/zenodo.5761752<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>References<\/p>\n","protected":false},"author":1,"featured_media":14119,"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-14118","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\/2025\/01\/Day-3a-0301.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14118","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=14118"}],"version-history":[{"count":1,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14118\/revisions"}],"predecessor-version":[{"id":14121,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14118\/revisions\/14121"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/14119"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}