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%I #14 Dec 10 2019 12:10:23
%S 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 33,36,23,54,81,32,19,50,75,28,35,42,63,40,55,26,39,60,37,90,135,48,
%U 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 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).
%C 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 1
%C |
%C ................../ \..................
%C 2 3
%C 4......../ \........5 6......../ \........9
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 8 7 10 15 12 11 18 27
%C 16 25 14 21 20 13 30 45 24 17 22 33 36 23 54 81
%C etc.
%C Note how all nodes with odd n have a right hand child with value 3n.
%H Antti Karttunen, <a href="/A269865/b269865.txt">Table of n, a(n) for n = 1..6142</a>
%H Antti Karttunen, <a href="/A135141/a135141.pdf">Entanglement Permutations</a>, 2016-2017
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).
%o (Scheme, with memoization-macro definec)
%o (definec (A269865 n) (cond ((<= n 1) n) ((even? n) (* 2 (A269865 (/ n 2)))) (else (A250469 (+ 1 (A269865 (/ (- n 1) 2)))))))
%Y Inverse: A269866.
%Y Cf. A250469.
%Y Related or similar permutations: A269359, A269863, A269864, A269867, A246375, A249814, A252755, A270195.
%K nonn,tabf,look
%O 1,2
%A _Antti Karttunen_, Mar 12 2016
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