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%I #9 Mar 25 2016 07:48:02
%S 1,2,9,3,11,12,36,4,15,14,39,17,40,52,108,5,16,22,51,20,47,59,114,25,
%T 55,60,118,77,167,156,312,6,18,24,54,30,73,75,165,28,67,68,139,85,185,
%U 166,339,34,84,80,174,87,187,173,347,117,227,254,496,236,461,475,852,7,21,26,56,33,76,79,170,43,99,112,216,115,219,251,490,41
%N Permutation of natural numbers: a(1) = 1, a(2n) = A270189(1+a(n)), a(2n+1) = A270190(a(n)).
%C This sequence can be represented as a binary tree. Each left hand child is produced as A270189(1+n), and each right hand child as A270190(n), when the parent node contains n:
%C 1
%C ................../ \..................
%C 2 9
%C 3......../ \........11 12......../ \........36
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 4 15 14 39 17 40 52 108
%C 5 16 22 51 20 47 59 114 25 55 60 118 77 167 156 312
%C etc.
%H Antti Karttunen, <a href="/A270202/b270202.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) = A270189(1+a(n)), a(2n+1) = A270190(a(n)).
%o (Scheme, with memoization-macro definec)
%o (definec (A270202 n) (cond ((= 1 n) n) ((even? n) (A270189 (+ 1 (A270202 (/ n 2))))) (else (A270190 (A270202 (/ (- n 1) 2))))))
%Y Inverse: A270201.
%Y Cf. A270189, A270190.
%Y Similar permutation: A270194.
%K nonn,tabf
%O 1,2
%A _Antti Karttunen_, Mar 16 2016
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