{"id":122,"date":"2021-12-08T20:18:03","date_gmt":"2021-12-08T23:18:03","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=122"},"modified":"2021-12-08T20:18:04","modified_gmt":"2021-12-08T23:18:04","slug":"crazy-running-equality-expressions-with-factorial-and-square-root","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=122","title":{"rendered":"Crazy Running Equality Expressions With Factorial and Square-Root"},"content":{"rendered":"\n<p>In&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/inderjtaneja.com\/2017\/05\/24\/running-expressions-increasing-and-decreasing-orders\/\" target=\"_blank\">previous works<\/a>, authors wrote equality expressions in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. These expressions are based on the idea of&nbsp;<strong>crazy representations<\/strong>&nbsp;of natural numbers. These equality expressions are based on basic operations along with&nbsp;<strong>factorial, square-root, Fibonacci sequence<\/strong>&nbsp;and&nbsp;<strong>triangular numbers values<\/strong>. These types of equalities, we called as&nbsp;<strong>crazy running equality expressions<\/strong>. This work is revised and enlarged version of author\u2019s previous works, where the basic operations along with factorial, square-root are considered. It is not possible to write all the natural numbers in terms of&nbsp;<strong>crazy running equality expressions<\/strong>. Only the possible numbers are written. The work is up to 6 digits:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Inder J. Taneja, Crazy Running Equality Expressions With Factorial and Square-Root,&nbsp;<strong>Zenodo<\/strong>, December 06, 2021, pp. 1-464,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5761752\"><strong>https:\/\/doi.org\/10.5281\/zenodo.5761752<\/strong><\/a><\/li><\/ul>\n\n\n\n<p>Link for download:<\/p>\n\n\n\n<p>See few examples below:<\/p>\n\n\n\n<figure class=\"wp-block-gallery columns-1 is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\"><ul class=\"blocks-gallery-grid\"><li class=\"blocks-gallery-item\"><figure><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"641\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-1-1024x641.png\" alt=\"\" data-id=\"123\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-1.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=123\" class=\"wp-image-123\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-1-1024x641.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-1-600x376.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-1-300x188.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-1-768x481.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-1-535x335.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-1.png 1383w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" width=\"1024\" height=\"729\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-2-1024x729.png\" alt=\"\" data-id=\"124\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-2.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=124\" class=\"wp-image-124\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-2-1024x729.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-2-600x427.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-2-300x214.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-2-768x547.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-2-535x381.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-2.png 1387w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" width=\"1024\" height=\"598\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-3-1024x598.png\" alt=\"\" data-id=\"125\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-3.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=125\" class=\"wp-image-125\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-3-1024x598.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-3-600x351.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-3-300x175.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-3-768x449.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-3-535x313.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-3.png 1388w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1022\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-1022x1024.png\" alt=\"\" data-id=\"126\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=126\" class=\"wp-image-126\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-1022x1024.png 1022w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-300x300.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-100x100.png 100w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-600x601.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-150x150.png 150w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-768x770.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-500x500.png 500w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-535x536.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4-256x256.png 256w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-4.png 1380w\" sizes=\"(max-width: 1022px) 100vw, 1022px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"792\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-5-1024x792.png\" alt=\"\" data-id=\"127\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-5.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=127\" class=\"wp-image-127\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-5-1024x792.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-5-600x464.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-5-300x232.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-5-768x594.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-5-535x414.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-5.png 1365w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"827\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6-1024x827.png\" alt=\"\" data-id=\"128\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=128\" class=\"wp-image-128\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6-1024x827.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6-600x484.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6-300x242.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6-768x620.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6-535x432.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6.png 1386w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"837\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7-837x1024.png\" alt=\"\" data-id=\"129\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=129\" class=\"wp-image-129\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7-837x1024.png 837w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7-600x734.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7-245x300.png 245w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7-768x940.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7-535x655.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7-1255x1536.png 1255w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-7.png 1382w\" sizes=\"(max-width: 837px) 100vw, 837px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"503\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-8-1024x503.png\" alt=\"\" data-id=\"130\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-8.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=130\" class=\"wp-image-130\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-8-1024x503.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-8-600x295.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-8-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-8-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-8-535x263.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-8.png 1381w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"904\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-9-1024x904.png\" alt=\"\" data-id=\"131\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-9.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=131\" class=\"wp-image-131\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-9-1024x904.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-9-600x529.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-9-300x265.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-9-768x678.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-9-535x472.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-9.png 1386w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"380\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-10-1024x380.png\" alt=\"\" data-id=\"132\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-10.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=132\" class=\"wp-image-132\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-10-1024x380.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-10-600x222.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-10-300x111.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-10-768x285.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-10-535x198.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-10.png 1381w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"788\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-11-788x1024.png\" alt=\"\" data-id=\"133\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-11.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=133\" class=\"wp-image-133\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-11-788x1024.png 788w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-11-600x780.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-11-231x300.png 231w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-11-768x998.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-11-535x695.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-11.png 1155w\" sizes=\"(max-width: 788px) 100vw, 788px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"836\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-12-836x1024.png\" alt=\"\" data-id=\"134\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-12.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=134\" class=\"wp-image-134\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-12-836x1024.png 836w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-12-600x735.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-12-245x300.png 245w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-12-768x940.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-12-535x655.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-12.png 1159w\" sizes=\"(max-width: 836px) 100vw, 836px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"936\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-13-1024x936.png\" alt=\"\" data-id=\"135\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-13.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=135\" class=\"wp-image-135\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-13-1024x936.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-13-600x549.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-13-300x274.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-13-768x702.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-13-535x489.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-13.png 1155w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"921\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-14-921x1024.png\" alt=\"\" data-id=\"136\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-14.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=136\" class=\"wp-image-136\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-14-921x1024.png 921w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-14-600x667.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-14-270x300.png 270w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-14-768x854.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-14-535x595.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-14.png 1158w\" sizes=\"(max-width: 921px) 100vw, 921px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"762\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-15-1024x762.png\" alt=\"\" data-id=\"137\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-15.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=137\" class=\"wp-image-137\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-15-1024x762.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-15-600x446.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-15-300x223.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-15-768x571.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-15-535x398.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-15.png 1159w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"950\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-16-1024x950.png\" alt=\"\" data-id=\"138\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-16.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=138\" class=\"wp-image-138\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-16-1024x950.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-16-600x557.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-16-300x278.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-16-768x712.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-16-535x496.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-16.png 1381w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"780\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-17-1024x780.png\" alt=\"\" data-id=\"139\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-17.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=139\" class=\"wp-image-139\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-17-1024x780.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-17-600x457.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-17-300x229.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-17-768x585.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-17-535x408.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-17.png 1383w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"860\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-18-1024x860.png\" alt=\"\" data-id=\"140\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-18.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=140\" class=\"wp-image-140\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-18-1024x860.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-18-600x504.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-18-300x252.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-18-768x645.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-18-535x450.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-18.png 1384w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"799\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19-799x1024.png\" alt=\"\" data-id=\"141\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=141\" class=\"wp-image-141\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19-799x1024.png 799w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19-600x769.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19-234x300.png 234w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19-768x984.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19-535x686.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19-1198x1536.png 1198w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-19.png 1384w\" sizes=\"(max-width: 799px) 100vw, 799px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"841\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20-841x1024.png\" alt=\"\" data-id=\"142\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=142\" class=\"wp-image-142\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20-841x1024.png 841w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20-600x731.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20-246x300.png 246w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20-768x935.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20-535x652.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20-1261x1536.png 1261w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-20.png 1381w\" sizes=\"(max-width: 841px) 100vw, 841px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"925\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-21-925x1024.png\" alt=\"\" data-id=\"143\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-21.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=143\" class=\"wp-image-143\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-21-925x1024.png 925w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-21-600x664.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-21-271x300.png 271w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-21-768x850.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-21-535x592.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-21.png 1380w\" sizes=\"(max-width: 925px) 100vw, 925px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"738\" height=\"1024\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22-738x1024.png\" alt=\"\" data-id=\"144\" data-full-url=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22.png\" data-link=\"https:\/\/numbers-magic.com\/?attachment_id=144\" class=\"wp-image-144\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22-738x1024.png 738w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22-600x833.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22-216x300.png 216w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22-768x1066.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22-535x742.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22-1107x1536.png 1107w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-22.png 1158w\" sizes=\"(max-width: 738px) 100vw, 738px\" \/><\/figure><\/li><\/ul><\/figure>\n\n\n\n<p><strong>Previous work for donwload:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Inder J. Taneja, Running Expressions in Increasing and Decreasing Orders of Natural Numbers Separated by Equality Signs, RGMIA Research Report Collection,&nbsp;<strong>18<\/strong>(2015), Article 27, pp.1-54,&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/rgmia.org\/papers\/v18\/v18a27.pdf\" target=\"_blank\"><strong>http:\/\/rgmia.org\/papers\/v18\/v18a27.pdf<\/strong><\/a>.<\/li><li>Inder J. Taneja, Running Expressions with Equalities: Increasing and Decreasing Orders \u2013 I, RGMIA Research Report Collection,&nbsp;<strong>20<\/strong>(2017), Art. 33, pp. 1-57,&nbsp;<a href=\"http:\/\/rgmia.org\/papers\/v20\/v20a33.pdf\"><strong>http:\/\/rgmia.org\/papers\/v20\/v20a33.pdf<\/strong><\/a>.<\/li><li>Inder J. Taneja, Running Expressions with Equalities: Increasing and Decreasing Orders \u2013 II, 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\"><strong>http:\/\/rgmia.org\/papers\/v20\/v20a34.pdf<\/strong><\/a>.<\/li><\/ul>\n\n\n\n<p><strong>Recent work for download:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Inder J. Taneja, Crazy Running Equality Expressions With Factorial and Square-Root,&nbsp;<strong>Zenodo<\/strong>, December 06, 2021, pp. 1-464,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5761752\"><strong>https:\/\/doi.org\/10.5281\/zenodo.5761752<\/strong><\/a><\/li><\/ul>\n\n\n\n<p><strong>Results with Fibonacci Squence and Triangular numbers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Inder J. Taneja, Fibonacci Sequence and Running Expressions with Equalities \u2013 I, RGMIA Research Report Collection,&nbsp;<strong>20<\/strong>(2017), Art. 35, pp. 1-83,&nbsp;&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/rgmia.org\/papers\/v20\/v20a35.pdf\" target=\"_blank\"><strong>http:\/\/rgmia.org\/papers\/v20\/v20a35.pdf<\/strong><\/a>.<\/li><li>Inder J. Taneja, Running Expressions with Triangular Numbers \u2013 I,&nbsp;&nbsp;<strong>Zenodo<\/strong>, December 21, 2018, pp. 1-142, &nbsp;<a href=\"http:\/\/doi.org\/10.5281\/zenodo.2483327\"><strong>http:\/\/doi.org\/10.5281\/zenodo.2483327<\/strong><\/a>.<\/li><\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In&nbsp;previous works, authors wrote equality expressions in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. These expressions are based on the idea of&nbsp;crazy representations&nbsp;of natural numbers. These equality expressions are based on basic operations along with&nbsp;factorial, square-root, Fibonacci sequence&nbsp;and&nbsp;triangular numbers values. These types [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":128,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[4],"tags":[],"class_list":["post-122","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-crazy-numbers"],"jetpack_featured_media_url":"https:\/\/numbers-magic.com\/wp-content\/uploads\/2021\/12\/Running-6.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/122","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=122"}],"version-history":[{"count":1,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/122\/revisions"}],"predecessor-version":[{"id":145,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/122\/revisions\/145"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/128"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}