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%I #9 Mar 25 2016 07:47:37
%S 1,2,3,4,5,6,9,7,10,8,12,11,15,16,30,13,17,18,31,14,26,20,34,19,33,23,
%T 45,24,48,46,93,21,40,25,49,27,50,47,94,22,41,39,80,29,61,54,99,28,52,
%U 53,97,36,68,69,124,37,70,73,154,71,127,141,266,32,65,60,112,38,78,74,155,42,85,75,158,72,133,142,267,35,67,62,113,59
%N Permutation of natural numbers: a(1) = 1, a(2n) = A269389(1+a(n)), a(2n+1) = A269399(a(n)).
%C This sequence can be represented as a binary tree. Each left hand child is produced as A269389(1+n), and each right hand child as A269399(n), when the parent node contains n:
%C 1
%C ................../ \..................
%C 2 3
%C 4......../ \........5 6......../ \........9
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 7 10 8 12 11 15 16 30
%C 13 17 18 31 14 26 20 34 19 33 23 45 24 48 46 93
%C etc.
%H Antti Karttunen, <a href="/A270194/b270194.txt">Table of n, a(n) for n = 1..8192</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) = A269389(1+a(n)), a(2n+1) = A269399(a(n)).
%o (Scheme, with memoization-macro definec)
%o (definec (A270194 n) (cond ((= 1 n) n) ((even? n) (A269389 (+ 1 (A270194 (/ n 2))))) (else (A269399 (A270194 (/ (- n 1) 2))))))
%Y Inverse: A270193.
%Y Cf. A269389, A269399.
%Y Similar permutations: A270199, A270202.
%K nonn,tabf
%O 1,2
%A _Antti Karttunen_, Mar 16 2016
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