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 A267112 #28 Sep 04 2016 17:21:20 %S A267112 1,2,3,4,5,7,6,8,9,12,10,15,13,14,11,16,17,21,18,27,22,24,19,31,28,29, %T A267112 23,30,25,26,20,32,33,38,34,48,39,42,35,58,49,51,40,54,43,45,36,63,59, %U A267112 60,50,61,52,53,41,62,55,56,44,57,46,47,37,64,65,71,66,86,72,76,67,106,87,90,73,96,77,80,68,121,107,109,88 %N A267112 Permutation of natural numbers: a(1) = 1; a(2n) = A087686(1+a(n)), a(2n+1) = A088359(a(n)), where A088359 and A087686 = numbers that occur only once (resp. more than once) in A004001. %C A267112 This sequence can be represented as a binary tree. Each left hand child is produced as A087686(1+n), and each right hand child as A088359(n), when their parent contains n: %C A267112 | %C A267112 ...................1................... %C A267112 2 3 %C A267112 4......../ \........5 7......../ \........6 %C A267112 / \ / \ / \ / \ %C A267112 / \ / \ / \ / \ %C A267112 / \ / \ / \ / \ %C A267112 8 9 12 10 15 13 14 11 %C A267112 16 17 21 18 27 22 24 19 31 28 29 23 30 25 26 20 %C A267112 etc. %C A267112 The level k of the tree contains all numbers of binary width k, like many base-2 related permutations (A003188, A054429, etc). For a proof, see A267110, which gives the contents of each parent node (for node containing n). %C A267112 A276442 shows the mirror-image of the same tree. %H A267112 Antti Karttunen, <a href="/A267112/b267112.txt">Table of n, a(n) for n = 1..8192</a> %H A267112 T. Kubo and R. Vakil, <a href="http://dx.doi.org/10.1016/0012-365X(94)00303-Z">On Conway's recursive sequence</a>, Discr. Math. 152 (1996), 225-252. %H A267112 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a> %H A267112 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %F A267112 a(1) = 1; after which, a(2n) = A087686(1+a(n)), a(2n+1) = A088359(a(n)). %F A267112 As a composition of other permutations: %F A267112 a(n) = A276442(A054429(n)). %F A267112 a(n) = A276344(A233276(n)). %F A267112 a(n) = A276346(A233278(n)). %F A267112 a(n) = A276446(A003188(n)). %F A267112 Other identities. For all n >= 0: %F A267112 a(2^n) = 2^n. [Follows from the properties (3) and (4) of A004001 given on page 227 of Kubo & Vakil paper.] %F A267112 a(A000225(n)) = A006127(n), i.e., a((2^(n+1)) - 1) = 2^n + n. [Numbers at the right edge.] %o A267112 (Scheme, with memoization-macro definec) %o A267112 (definec (A267112 n) (cond ((< n 2) n) ((even? n) (A087686 (+ 1 (A267112 (/ n 2))))) (else (A088359 (A267112 (/ (- n 1) 2)))))) %Y A267112 Inverse: A267111. %Y A267112 Cf. A000079, A000225, A004001, A006127, A087686, A088359, A267110. %Y A267112 Similar or related permutations: A003188, A054429, A276442, A233276, A233278, A276344, A276346, A276446. %Y A267112 Cf. also permutations A266411, A266412 and arrays A265901, A265903. %K A267112 nonn,tabf,look %O A267112 1,2 %A A267112 _Antti Karttunen_, Jan 10 2016