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 A284572 #10 Apr 17 2017 09:02:03 %S A284572 1,2,4,3,9,6,25,5,8,14,20,10,49,39,52,7,12,13,27,22,45,33,63,15,121, %T A284572 79,80,65,50,85,2809,11,16,19,169,21,28,42,56,35,529,73,92,55,68,103, %U A284572 128,23,32,199,244,130,100,131,243,106,132,82,153,139,172,4619,5620,17,18,26,289,31,40,277,340,34,44,43,841,69,1849,91,171,58,48 %N A284572 Permutation of natural numbers: a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A065642(1+a(n)). %C A284572 This sequence can be represented as a binary tree. Each left hand child is produced as A005117(1+n), and each right hand child as A065642(1+n), when the parent node contains n: %C A284572 1 %C A284572 ................../ \.................. %C A284572 2 4 %C A284572 3......../ \........9 6......../ \........25 %C A284572 / \ / \ / \ / \ %C A284572 / \ / \ / \ / \ %C A284572 / \ / \ / \ / \ %C A284572 5 8 14 20 10 49 39 52 %C A284572 7 12 13 27 22 45 33 63 15 121 79 80 65 50 85 2809 %C A284572 etc. %C A284572 Compare to A285112. %H A284572 Antti Karttunen, <a href="/A284572/b284572.txt">Table of n, a(n) for n = 1..166</a> %H A284572 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %F A284572 a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A065642(1+a(n)). %o A284572 (Scheme, with memoization-macro definec) %o A284572 (definec (A284572 n) (cond ((= 1 n) n) ((even? n) (A005117 (+ 1 (A284572 (/ n 2))))) (else (A065642 (+ 1 (A284572 (/ (- n 1) 2))))))) %Y A284572 Inverse: A284571. %Y A284572 Cf. A005117, A065642. %Y A284572 Similar or related permutations: A243344, A243346, A277696, A285112. %K A284572 nonn,tabf %O A284572 1,2 %A A284572 _Antti Karttunen_, Apr 17 2017