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%I #9 Dec 13 2023 08:21:15
%S 1,2,3,4,5,6,9,10,7,8,15,16,11,26,27,28,13,12,21,22,25,36,45,46,19,14,
%T 33,76,65,66,81,82,31,18,39,34,17,56,63,64,29,50,75,106,41,116,135,
%U 136,53,24,57,40,35,86,99,226,143,120,195,196,71,206,243,244,89,38,93,52,23,96,117,100,77,20,51,166,145,156,189,190,119,32,87
%N Permutation of natural numbers: a(1) = 1, a(2n) = A269360(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 A269360(n) [= 1+A250469(n)] and the right hand child contains A250469(1+n):
%C 1
%C |
%C ................../ \..................
%C 2 3
%C 4......../ \........5 6......../ \........9
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 10 7 8 15 16 11 26 27
%C 28 13 12 21 22 25 36 45 46 19 14 33 76 65 66 81
%C etc.
%H Antti Karttunen, <a href="/A269864/b269864.txt">Table of n, a(n) for n = 1..5887</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, a(2n) = 1 + A250469(a(n)), a(2n+1) = A250469(1+a(n)).
%o (Scheme, with memoization-macro definec)
%o (definec (A269864 n) (cond ((= 1 n) 1) ((even? n) (+ 1 (A250469 (A269864 (/ n 2))))) (else (A250469 (+ 1 (A269864 (/ (- n 1) 2)))))))
%Y Inverse: A269863.
%Y Cf. A250469, A269360.
%Y Cf. also A269865, A269866, A269867.
%Y Differs from similarly constructed A245606 for the first time at n=15, where a(15)=27 instead of 21.
%K nonn,tabf
%O 1,2
%A _Antti Karttunen_, Mar 13 2016
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