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A260432 Permutation of natural numbers: a(1) = 1, a(2n) = A257804(a(n)), a(2n+1) = A257803(1+a(n)), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.

%I A260432 #9 Jul 27 2015 22:14:45
%S A260432 1,2,4,3,7,6,12,5,9,11,21,10,18,19,30,8,17,14,24,16,27,36,54,15,25,31,
%T A260432 49,32,52,48,74,13,23,29,42,22,35,40,60,28,41,45,68,61,83,92,132,26,
%U A260432 38,43,64,50,75,86,119,51,76,89,128,85,118,125,172,20,34,39,57,47,73,71,106,37,55,59,82,67,96,101,140,46,70,69
%N A260432 Permutation of natural numbers: a(1) = 1, a(2n) = A257804(a(n)), a(2n+1) = A257803(1+a(n)), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.
%C A260432 This sequence can be represented as a binary tree. Each left hand child is produced as A257804(n), and each right hand child as A257803(1+n), when the parent contains n:
%C A260432                                      |
%C A260432                   ...................1...................
%C A260432                  2                                       4
%C A260432        3......../ \........7                   6......../ \........12
%C A260432       / \                 / \                 / \                 / \
%C A260432      /   \               /   \               /   \               /   \
%C A260432     /     \             /     \             /     \             /     \
%C A260432    5       9          11       21         10       18         19       30
%C A260432   8 17   14 24      16  27   36  54     15  25   31  49     32  52   48  74
%C A260432 etc.
%H A260432 Antti Karttunen, <a href="/A260432/b260432.txt">Table of n, a(n) for n = 1..8191</a>
%H A260432 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A260432 a(1) = 1, a(2n) = A257804(a(n)), a(2n+1) = A257803(1+a(n)).
%F A260432 As a composition of other permutations:
%F A260432 a(n) = A260434(A054429(n)).
%F A260432 a(n) = A260430(A260434(n)).
%o A260432 (Scheme, with memoizing macro definec)
%o A260432 (definec (A260432 n) (cond ((<= n 1) n) ((even? n) (A257804 (A260432 (/ n 2)))) (else (A257803 (+ 1 (A260432 (/ (- n 1) 2)))))))
%Y A260432 Inverse: A260431.
%Y A260432 Related permutations: A260434, A260430, A054429.
%Y A260432 Cf. A257803, A257804, A257807, A257808.
%Y A260432 Cf. also A233271, A257806.
%K A260432 nonn,tabf
%O A260432 1,2
%A A260432 _Antti Karttunen_, Jul 27 2015