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A260434 Permutation of natural numbers: a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.

%I A260434 #14 Jul 28 2015 05:37:36
%S A260434 1,4,2,12,6,7,3,30,19,18,10,21,11,9,5,74,48,52,32,49,31,25,15,54,36,
%T A260434 27,16,24,14,17,8,172,125,118,85,128,89,76,51,119,86,75,50,64,43,38,
%U A260434 26,132,92,83,61,68,45,41,28,60,40,35,22,42,29,23,13,383,314,275,219,266,208,201,152,283,227,207,159,174,129,127,88
%N A260434 Permutation of natural numbers: a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.
%C A260434 This sequence can be represented as a binary tree. Each left hand child is produced as A257803(1+n), and each right hand child as A257804(n), when the parent contains n:
%C A260434                                      |
%C A260434                   ...................1...................
%C A260434                  4                                       2
%C A260434       12......../ \........6                   7......../ \........3
%C A260434       / \                 / \                 / \                 / \
%C A260434      /   \               /   \               /   \               /   \
%C A260434     /     \             /     \             /     \             /     \
%C A260434   30       19         18       10         21       11          9       5
%C A260434 74  48   52  32     49  31   25  15     54  36   27  16      24 14   17 8
%C A260434 etc.
%C A260434 Note how this is a mirror image of the tree shown in A260432.
%H A260434 Antti Karttunen, <a href="/A260434/b260434.txt">Table of n, a(n) for n = 1..16383</a>
%H A260434 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A260434 a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)).
%F A260434 As a composition of other permutations:
%F A260434 a(n) = A260432(A054429(n)).
%F A260434 a(n) = A260430(A260432(n)).
%o A260434 (Scheme, with memoizing macro definec)
%o A260434 (definec (A260434 n) (cond ((<= n 1) n) ((even? n) (A257803 (+ 1 (A260434 (/ n 2))))) (else (A257804 (A260434 (/ (- n 1) 2))))))
%Y A260434 Inverse: A260433.
%Y A260434 Related permutations: A260432, A260430, A054429.
%Y A260434 Cf. A257803, A257804, A257807, A257808.
%Y A260434 Cf. also A233271, A257806.
%K A260434 nonn,tabf,look
%O A260434 1,2
%A A260434 _Antti Karttunen_, Jul 27 2015