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Permutation of natural numbers: a(1) = 1, a(2n) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).
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%I #6 Feb 13 2016 23:17:58

%S 1,2,3,6,4,9,5,13,11,10,7,21,18,12,8,29,23,25,20,24,19,14,15,45,40,39,

%T 34,28,22,17,16,62,56,49,42,54,48,44,37,51,47,43,36,30,26,33,27,95,87,

%U 84,75,80,74,73,65,61,53,46,41,38,32,35,31,129,120,115,108,100,93,88,82,112,105,99,92,94,86,78,70

%N Permutation of natural numbers: a(1) = 1, a(2n) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).

%C This sequence can be represented as a binary tree. Each left hand child is produced as A268677(n), and each right hand child as A268678(1+n), when the parent node contains n:

%C |

%C ...................1...................

%C 2 3

%C 6......../ \........4 9......../ \........5

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C 13 11 10 7 21 18 12 8

%C 29 23 25 20 24 19 14 15 45 40 39 34 28 22 17 16

%C etc.

%H Antti Karttunen, <a href="/A268712/b268712.txt">Table of n, a(n) for n = 1..16383</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(1) = 1, after which: a(2n) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).

%o (Scheme, with memoization-macro definec)

%o (definec (A268712 n) (cond ((= 1 n) n) ((even? n) (A268677 (A268712 (/ n 2)))) (else (A268678 (+ 1 (A268712 (/ (- n 1) 2)))))))

%Y Inverse: A268711.

%Y Cf. A268677, A268678.

%K nonn,tabf

%O 1,2

%A _Antti Karttunen_, Feb 11 2016