This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A233278 #20 Apr 19 2015 20:49:51 %S A233278 0,1,2,3,5,4,6,7,12,10,9,8,13,11,14,15,27,23,21,19,20,18,17,16,28,25, %T A233278 24,22,29,26,30,31,58,53,48,46,44,41,40,38,43,39,37,35,36,34,33,32,59, %U A233278 54,52,49,51,47,45,42,60,56,55,50,61,57,62,63,121,113,108 %N A233278 a(0)=0, a(1)=1, after which a(2n) = A055938(a(n)), a(2n+1) = A005187(1+a(n)). %C A233278 This permutation is obtained by "entangling" even and odd numbers with complementary pair A055938 & A005187, meaning that it can be viewed as a binary tree. Each child to the left is obtained by applying A055938(n) to the parent node containing n, and each child to the right is obtained as A005187(n+1): %C A233278 0 %C A233278 | %C A233278 ...................1................... %C A233278 2 3 %C A233278 5......../ \........4 6......../ \........7 %C A233278 / \ / \ / \ / \ %C A233278 / \ / \ / \ / \ %C A233278 / \ / \ / \ / \ %C A233278 12 10 9 8 13 11 14 15 %C A233278 27 23 21 19 20 18 17 16 28 25 24 22 29 26 30 31 %C A233278 etc. %C A233278 For n >= 1, A256991(n) gives the contents of the immediate parent node of the node containing n, while A070939(n) gives the total distance to zero at the root from the node containing n, with A256478(n) telling how many of the terms encountered on that journey are terms of A005187 (including the penultimate 1 but not the final 0 in the count), while A256479(n) tells how many of them are terms of A055938. %C A233278 Permutation A233276 gives the mirror image of the same tree. %H A233278 Antti Karttunen, <a href="/A233278/b233278.txt">Table of n, a(n) for n = 0..8191</a> %H A233278 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %F A233278 a(0)=0, a(1)=1, and thereafter, a(2n) = A055938(a(n)), a(2n+1) = A005187(1+a(n)). %F A233278 As a composition of related permutations: %F A233278 a(n) = A233276(A054429(n)). %o A233278 (Scheme, with memoizing definec-macro from _Antti Karttunen_'s IntSeq-library) %o A233278 (definec (A233278 n) (cond ((< n 2) n) ((even? n) (A055938 (A233278 (/ n 2)))) (else (A005187 (+ 1 (A233278 (/ (- n 1) 2))))))) %Y A233278 Inverse permutation: A233277. %Y A233278 Cf. A005187, A054429, A055938, A256991, A256478, A256479. %Y A233278 Cf. also A070939 (the binary width of both n and a(n)). %Y A233278 Related arrays: A255555, A255557. %Y A233278 Similarly constructed permutation pairs: A005940/A156552, A135141/A227413, A232751/A232752, A233275/A233276, A233279/A233280, A003188/A006068. %K A233278 nonn,tabf %O A233278 0,3 %A A233278 _Antti Karttunen_, Dec 18 2013 %E A233278 Name changed and the illustration of binary tree added by _Antti Karttunen_, Apr 19 2015