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A269865 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

%I A269865 #14 Dec 10 2019 12:10:23
%S A269865 1,2,3,4,5,6,9,8,7,10,15,12,11,18,27,16,25,14,21,20,13,30,45,24,17,22,
%T A269865 33,36,23,54,81,32,19,50,75,28,35,42,63,40,55,26,39,60,37,90,135,48,
%U A269865 49,34,51,44,29,66,99,72,41,46,69,108,91,162,243,64,85,38,57,100,125,150,225,56,31,70,105,84,47,126,189,80,43,110,165,52
%N A269865 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).
%C A269865 This sequence can be represented as a binary tree. When the parent contains n, the left hand child contains 2n, while the value of right hand child is obtained by applying A250469(1+n):
%C A269865                                     1
%C A269865                                     |
%C A269865                  ................../ \..................
%C A269865                 2                                       3
%C A269865       4......../ \........5                   6......../ \........9
%C A269865      / \                 / \                 / \                 / \
%C A269865     /   \               /   \               /   \               /   \
%C A269865    /     \             /     \             /     \             /     \
%C A269865   8       7          10       15         12       11         18       27
%C A269865 16 25   14 21      20  13   30  45     24  17   22  33     36  23   54  81
%C A269865 etc.
%C A269865 Note how all nodes with odd n have a right hand child with value 3n.
%H A269865 Antti Karttunen, <a href="/A269865/b269865.txt">Table of n, a(n) for n = 1..6142</a>
%H A269865 Antti Karttunen, <a href="/A135141/a135141.pdf">Entanglement Permutations</a>, 2016-2017
%H A269865 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A269865 a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).
%o A269865 (Scheme, with memoization-macro definec)
%o A269865 (definec (A269865 n) (cond ((<= n 1) n) ((even? n) (* 2 (A269865 (/ n 2)))) (else (A250469 (+ 1 (A269865 (/ (- n 1) 2)))))))
%Y A269865 Inverse: A269866.
%Y A269865 Cf. A250469.
%Y A269865 Related or similar permutations: A269359, A269863, A269864, A269867, A246375, A249814, A252755, A270195.
%K A269865 nonn,tabf,look
%O A269865 1,2
%A A269865 _Antti Karttunen_, Mar 12 2016