{"id":516,"date":"2020-08-08T04:55:32","date_gmt":"2020-08-08T04:55:32","guid":{"rendered":"http:\/\/soulofmathematics.com\/?p=516"},"modified":"2020-10-03T09:02:48","modified_gmt":"2020-10-03T03:32:48","slug":"the-recaman-sequence","status":"publish","type":"post","link":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/","title":{"rendered":"The Recam\u00e1n Sequence"},"content":{"rendered":"\n<p>Recam\u00e1n&#8217;s sequence was named after its inventor, Colombian mathematician Bernardo Recam\u00e1n Santos, by&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Neil_Sloane\">Neil Sloane<\/a>, creator of the&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/oeis.org\/A005132\" target=\"_blank\">On-Line Encyclopedia of Integer Sequences (OEIS)<\/a>. It is a well known <strong>sequence<\/strong>&nbsp;defined by a recurrence relation. In computer science they are often defined by recursion. <\/p>\n\n\n\n<p>The Recam\u00e1n Sequence is defined by-<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/89ab504e66d289aeb91cdd3c9b3d88212a13f506\" alt=\"{\\displaystyle a_{n}={\\begin{cases}0&amp;&amp;{\\text{if }}n=0\\\\a_{n-1}-n&amp;&amp;{\\text{if }}a_{n-1}-n&gt;0{\\text{ and is not already in the sequence}}\\\\a_{n-1}+n&amp;&amp;{\\text{otherwise}}\\end{cases}}}\" width=\"674\" height=\"81\"\/><\/figure>\n\n\n\n<p>According to this sequence first few elements are-                                              0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 42, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 87, 29, 88, 28, 89, 27, 90, 26, 91, 157, 224&#8230;<\/p>\n\n\n\n<p>The sequence satisfies<img decoding=\"async\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/9919dc647332358329ca73c754aed0edca83f2ea\" alt=\"{\\displaystyle a_{n}\\geq 0}\"> <img decoding=\"async\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/1cfdecdd59f0318657dcbd5a2294725a47e458d4\" alt=\"{\\displaystyle |a_{n}-a_{n-1}|=n}\"> This is not a permutation of the integers: the first repeated term is&nbsp;<img decoding=\"async\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0734e4d14b32b381659d207ff285de09e0ac18cc\" alt=\"{\\displaystyle 42=a_{24}=a_{20}}\"> Another one is&nbsp;<img decoding=\"async\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/59e4c325ce4ec17b819f3fad031e928f9f03db40\" alt=\"{\\displaystyle 43=a_{18}=a_{26}}\"> <a href=\"https:\/\/en.wikipedia.org\/wiki\/Neil_Sloane\">Neil Sloane<\/a>&nbsp;has conjectured that every number eventually appears,&nbsp;but it has not been proved. Even though 10<sup>15<\/sup>&nbsp;terms have been calculated (in 2018), the number 852,655 has not appeared on the list.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"512\" height=\"324\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/rec.jpg?resize=512%2C324&#038;ssl=1\" alt=\"recaman sequence\" class=\"wp-image-527\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/rec.jpg?w=512&amp;ssl=1 512w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/rec.jpg?resize=300%2C190&amp;ssl=1 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><figcaption>Credits: <a rel=\"noreferrer noopener\" href=\"https:\/\/oeis.org\/A005132\" target=\"_blank\">On-Line Encyclopedia of Integer Sequences (OEIS)<\/a><\/figcaption><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">MATLAB CODE FOR Recam\u00e1n Sequence<\/h5>\n\n\n\n<pre class=\"wp-block-preformatted\">n=65; % Number of Terms in the Sequence\nA = zeros(1,n);\nA(1) = 0;\nfor ii = 1:n-1 % Algorithm to create the sequence\nb = A(ii)-ii;\nA(ii+1) = b + 2*ii;\nif b &gt; 0 &amp;&amp; ~any(A == b)\nA(ii + 1) = b;\nend\nend\nhold on;\naxis equal;\nfor i = 2:1:n % Plotting the Graphs\ny = 0; x = (A(i)+A(i-1))\/2; r = (A(i)-A(i-1))\/2;\nth = 0:pi\/50:pi;\nif A(i)&gt;A(i-1)\nxunit = r * cos(th) + x;\nyunit = r * sin(th) + y;\nend\nif A(i)&lt;A(i-1)\nxunit = -r * cos(th) + x;\nyunit = -r * sin(th) + y;\nend\nif mod(i,2) == 0\nh = plot(xunit, -yunit,'k');\nelse\nh = plot(xunit, yunit,'k');\nend\nend<\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"680\" height=\"427\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/Screenshot-76.png?resize=680%2C427&#038;ssl=1\" alt=\"\" class=\"wp-image-528\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/Screenshot-76.png?w=680&amp;ssl=1 680w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/Screenshot-76.png?resize=300%2C188&amp;ssl=1 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><figcaption>MATLAB PLOT<\/figcaption><\/figure>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/soulofmathematics.com\/index.php\/all-posts\/\">All Posts<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Recam\u00e1n&#8217;s sequence was named after its inventor, Colombian mathematician Bernardo Recam\u00e1n Santos, by&nbsp;Neil Sloane, creator of the&nbsp;On-Line Encyclopedia of Integer Sequences (OEIS). It is a well known sequence&nbsp;defined by a recurrence relation. In computer science they are often defined by recursion. The Recam\u00e1n Sequence is defined by- According to this sequence first few elements are- 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 42, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 87, 29, 88, 28, 89, 27, 90, 26, 91, 157, 224&#8230; The sequence satisfies This is not a permutation of the integers: the first repeated term is&nbsp; Another one is&nbsp; Neil Sloane&nbsp;has conjectured that every number eventually appears,&nbsp;but it has not been proved. Even though 1015&nbsp;terms have been calculated (in 2018), the number 852,655 has not appeared on the list. MATLAB CODE FOR Recam\u00e1n Sequence n=65; % Number of Terms in the Sequence A = zeros(1,n); A(1) = 0; for ii = 1:n-1 % Algorithm to create the sequence b = A(ii)-ii; A(ii+1) = b + 2*ii; if b &gt; 0 &amp;&amp; ~any(A == b) A(ii + 1) = b; end end hold on; axis equal; for i = 2:1:n % Plotting the Graphs y = 0; x = (A(i)+A(i-1))\/2; r = (A(i)-A(i-1))\/2; th = 0:pi\/50:pi; if A(i)&gt;A(i-1) xunit = r * cos(th) + x; yunit = r * sin(th) + y; end if A(i)&lt;A(i-1) xunit = -r * cos(th) + x; yunit = -r * sin(th) + y; end if mod(i,2) == 0 h = plot(xunit, -yunit,&#8217;k&#8217;); else h = plot(xunit, yunit,&#8217;k&#8217;); end end<\/p>\n","protected":false},"author":1,"featured_media":518,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[6,7,5,4],"class_list":["post-516","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sneak-peeks","tag-bernardo-recaman-santos","tag-computer-science","tag-neil-sloane","tag-the-recaman-sequence"],"featured_image_src":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1","blog_images":{"medium":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=300%2C225&ssl=1","large":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1"},"ams_acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The Recam\u00e1n Sequence - SOUL OF MATHEMATICS<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Recam\u00e1n Sequence - SOUL OF MATHEMATICS\" \/>\n<meta property=\"og:description\" content=\"Recam\u00e1n&#8217;s sequence was named after its inventor, Colombian mathematician Bernardo Recam\u00e1n Santos, by&nbsp;Neil Sloane, creator of the&nbsp;On-Line Encyclopedia of Integer Sequences (OEIS). It is a well known sequence&nbsp;defined by a recurrence relation. In computer science they are often defined by recursion. The Recam\u00e1n Sequence is defined by- According to this sequence first few elements are- 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 42, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 87, 29, 88, 28, 89, 27, 90, 26, 91, 157, 224&#8230; The sequence satisfies This is not a permutation of the integers: the first repeated term is&nbsp; Another one is&nbsp; Neil Sloane&nbsp;has conjectured that every number eventually appears,&nbsp;but it has not been proved. Even though 1015&nbsp;terms have been calculated (in 2018), the number 852,655 has not appeared on the list. MATLAB CODE FOR Recam\u00e1n Sequence n=65; % Number of Terms in the Sequence A = zeros(1,n); A(1) = 0; for ii = 1:n-1 % Algorithm to create the sequence b = A(ii)-ii; A(ii+1) = b + 2*ii; if b &gt; 0 &amp;&amp; ~any(A == b) A(ii + 1) = b; end end hold on; axis equal; for i = 2:1:n % Plotting the Graphs y = 0; x = (A(i)+A(i-1))\/2; r = (A(i)-A(i-1))\/2; th = 0:pi\/50:pi; if A(i)&gt;A(i-1) xunit = r * cos(th) + x; yunit = r * sin(th) + y; end if A(i)&lt;A(i-1) xunit = -r * cos(th) + x; yunit = -r * sin(th) + y; end if mod(i,2) == 0 h = plot(xunit, -yunit,&#039;k&#039;); else h = plot(xunit, yunit,&#039;k&#039;); end end\" \/>\n<meta property=\"og:url\" content=\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/\" \/>\n<meta property=\"og:site_name\" content=\"SOUL OF MATHEMATICS\" \/>\n<meta property=\"article:published_time\" content=\"2020-08-08T04:55:32+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-10-03T03:32:48+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/i1.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1\" \/>\n\t<meta property=\"og:image:width\" content=\"800\" \/>\n\t<meta property=\"og:image:height\" content=\"600\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/gif\" \/>\n<meta name=\"author\" content=\"Rajarshi Dey\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Rajarshi Dey\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/\",\"url\":\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/\",\"name\":\"The Recam\u00e1n Sequence - SOUL OF MATHEMATICS\",\"isPartOf\":{\"@id\":\"https:\/\/soulofmathematics.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1\",\"datePublished\":\"2020-08-08T04:55:32+00:00\",\"dateModified\":\"2020-10-03T03:32:48+00:00\",\"author\":{\"@id\":\"https:\/\/soulofmathematics.com\/#\/schema\/person\/c61ee309ed66bc94ba7a27f6129b945c\"},\"breadcrumb\":{\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#primaryimage\",\"url\":\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1\",\"contentUrl\":\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1\",\"width\":800,\"height\":600,\"caption\":\"recaman sequence\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/soulofmathematics.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"The Recam\u00e1n Sequence\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/soulofmathematics.com\/#website\",\"url\":\"https:\/\/soulofmathematics.com\/\",\"name\":\"SOUL OF MATHEMATICS\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/soulofmathematics.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/soulofmathematics.com\/#\/schema\/person\/c61ee309ed66bc94ba7a27f6129b945c\",\"name\":\"Rajarshi Dey\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/soulofmathematics.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/14acfcec71e13078f5b322bb6adfd1f6579c091317d0e0077c2311511263a8b0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/14acfcec71e13078f5b322bb6adfd1f6579c091317d0e0077c2311511263a8b0?s=96&d=mm&r=g\",\"caption\":\"Rajarshi Dey\"},\"sameAs\":[\"http:\/\/soulofmathematics.com\"],\"url\":\"https:\/\/soulofmathematics.com\/index.php\/author\/rajarshidey1729gmail-com\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"The Recam\u00e1n Sequence - SOUL OF MATHEMATICS","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/","og_locale":"en_US","og_type":"article","og_title":"The Recam\u00e1n Sequence - SOUL OF MATHEMATICS","og_description":"Recam\u00e1n&#8217;s sequence was named after its inventor, Colombian mathematician Bernardo Recam\u00e1n Santos, by&nbsp;Neil Sloane, creator of the&nbsp;On-Line Encyclopedia of Integer Sequences (OEIS). It is a well known sequence&nbsp;defined by a recurrence relation. In computer science they are often defined by recursion. The Recam\u00e1n Sequence is defined by- According to this sequence first few elements are- 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 42, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 87, 29, 88, 28, 89, 27, 90, 26, 91, 157, 224&#8230; The sequence satisfies This is not a permutation of the integers: the first repeated term is&nbsp; Another one is&nbsp; Neil Sloane&nbsp;has conjectured that every number eventually appears,&nbsp;but it has not been proved. Even though 1015&nbsp;terms have been calculated (in 2018), the number 852,655 has not appeared on the list. MATLAB CODE FOR Recam\u00e1n Sequence n=65; % Number of Terms in the Sequence A = zeros(1,n); A(1) = 0; for ii = 1:n-1 % Algorithm to create the sequence b = A(ii)-ii; A(ii+1) = b + 2*ii; if b &gt; 0 &amp;&amp; ~any(A == b) A(ii + 1) = b; end end hold on; axis equal; for i = 2:1:n % Plotting the Graphs y = 0; x = (A(i)+A(i-1))\/2; r = (A(i)-A(i-1))\/2; th = 0:pi\/50:pi; if A(i)&gt;A(i-1) xunit = r * cos(th) + x; yunit = r * sin(th) + y; end if A(i)&lt;A(i-1) xunit = -r * cos(th) + x; yunit = -r * sin(th) + y; end if mod(i,2) == 0 h = plot(xunit, -yunit,'k'); else h = plot(xunit, yunit,'k'); end end","og_url":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/","og_site_name":"SOUL OF MATHEMATICS","article_published_time":"2020-08-08T04:55:32+00:00","article_modified_time":"2020-10-03T03:32:48+00:00","og_image":[{"width":800,"height":600,"url":"https:\/\/i1.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1","type":"image\/gif"}],"author":"Rajarshi Dey","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Rajarshi Dey","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/","url":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/","name":"The Recam\u00e1n Sequence - SOUL OF MATHEMATICS","isPartOf":{"@id":"https:\/\/soulofmathematics.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#primaryimage"},"image":{"@id":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#primaryimage"},"thumbnailUrl":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1","datePublished":"2020-08-08T04:55:32+00:00","dateModified":"2020-10-03T03:32:48+00:00","author":{"@id":"https:\/\/soulofmathematics.com\/#\/schema\/person\/c61ee309ed66bc94ba7a27f6129b945c"},"breadcrumb":{"@id":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#primaryimage","url":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1","contentUrl":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1","width":800,"height":600,"caption":"recaman sequence"},{"@type":"BreadcrumbList","@id":"https:\/\/soulofmathematics.com\/index.php\/the-recaman-sequence\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/soulofmathematics.com\/"},{"@type":"ListItem","position":2,"name":"The Recam\u00e1n Sequence"}]},{"@type":"WebSite","@id":"https:\/\/soulofmathematics.com\/#website","url":"https:\/\/soulofmathematics.com\/","name":"SOUL OF MATHEMATICS","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/soulofmathematics.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/soulofmathematics.com\/#\/schema\/person\/c61ee309ed66bc94ba7a27f6129b945c","name":"Rajarshi Dey","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/soulofmathematics.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/14acfcec71e13078f5b322bb6adfd1f6579c091317d0e0077c2311511263a8b0?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/14acfcec71e13078f5b322bb6adfd1f6579c091317d0e0077c2311511263a8b0?s=96&d=mm&r=g","caption":"Rajarshi Dey"},"sameAs":["http:\/\/soulofmathematics.com"],"url":"https:\/\/soulofmathematics.com\/index.php\/author\/rajarshidey1729gmail-com\/"}]}},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/recaman-2.gif?fit=800%2C600&ssl=1","jetpack-related-posts":[],"jetpack_shortlink":"https:\/\/wp.me\/pcfs4y-8k","_links":{"self":[{"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/posts\/516","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/comments?post=516"}],"version-history":[{"count":1,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/posts\/516\/revisions"}],"predecessor-version":[{"id":1612,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/posts\/516\/revisions\/1612"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/media\/518"}],"wp:attachment":[{"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/media?parent=516"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/categories?post=516"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/tags?post=516"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}