{"id":1174,"date":"2019-10-25T14:10:37","date_gmt":"2019-10-25T14:10:37","guid":{"rendered":"https:\/\/muthu.co\/?p=1174"},"modified":"2021-05-24T02:40:18","modified_gmt":"2021-05-24T02:40:18","slug":"function-to-get-the-preceding-odd-number-y-for-any-given-number-x","status":"publish","type":"post","link":"http:\/\/write.muthu.co\/function-to-get-the-preceding-odd-number-y-for-any-given-number-x\/","title":{"rendered":"Function to get the preceding odd number (y) for any given number (x)"},"content":{"rendered":"\n<p>For any function,<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_23.png\"><img loading=\"lazy\" decoding=\"async\" width=\"198\" height=\"237\" src=\"https:\/\/muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_23.png\" alt=\"\" class=\"wp-image-1176\"\/><\/a><\/figure><\/div>\n\n\n\n<p>We want, for every value of x, return the corresponding odd number. If x is odd then return it as it is, else return the next number. This can easily be done using a computer program by checking if the number is odd or even. But if you had to find a general formula we would need the help of some basic maths.<\/p>\n\n\n\n<p>Let&#8217;s decompose our above function and see what we can extract.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_26.png\"><img loading=\"lazy\" decoding=\"async\" width=\"136\" height=\"207\" src=\"https:\/\/muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_26.png\" alt=\"\" class=\"wp-image-1177\"\/><\/a><\/figure><\/div>\n\n\n\n<p>We just need to find a general formula for the second digit on the RHS which is alternating between 0 and 1. Our function now looks like:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_28.png\"><img loading=\"lazy\" decoding=\"async\" width=\"145\" height=\"212\" src=\"https:\/\/muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_28.png\" alt=\"\" class=\"wp-image-1178\"\/><\/a><\/figure><\/div>\n\n\n\n<p>The series 0,1,0,1.. can be easily represented by the below formula:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_33.png\"><img loading=\"lazy\" decoding=\"async\" width=\"403\" height=\"217\" src=\"https:\/\/muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_33.png\" alt=\"\" class=\"wp-image-1182\" srcset=\"http:\/\/write.muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_33.png 403w, http:\/\/write.muthu.co\/wp-content\/uploads\/2019\/10\/Snip20191025_33-300x162.png 300w\" sizes=\"auto, (max-width: 403px) 100vw, 403px\" \/><\/a><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>For any function, We want, for every value of x, return the corresponding odd number. If x is odd then return it as it is, else return the next number. This can easily be done using a computer program by checking if the number is odd or even. But if you had to find a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1182,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[54],"class_list":["post-1174","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-mathematics"],"_links":{"self":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/1174","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/comments?post=1174"}],"version-history":[{"count":3,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/1174\/revisions"}],"predecessor-version":[{"id":1857,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/1174\/revisions\/1857"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/media\/1182"}],"wp:attachment":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/media?parent=1174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/categories?post=1174"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/tags?post=1174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}