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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.
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%I #9 Jul 27 2015 22:14:45

%S 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 49,32,52,48,74,13,23,29,42,22,35,40,60,28,41,45,68,61,83,92,132,26,

%U 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 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 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 |

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

%C 2 4

%C 3......../ \........7 6......../ \........12

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C 5 9 11 21 10 18 19 30

%C 8 17 14 24 16 27 36 54 15 25 31 49 32 52 48 74

%C etc.

%H Antti Karttunen, <a href="/A260432/b260432.txt">Table of n, a(n) for n = 1..8191</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) = A257804(a(n)), a(2n+1) = A257803(1+a(n)).

%F As a composition of other permutations:

%F a(n) = A260434(A054429(n)).

%F a(n) = A260430(A260434(n)).

%o (Scheme, with memoizing macro definec)

%o (definec (A260432 n) (cond ((<= n 1) n) ((even? n) (A257804 (A260432 (/ n 2)))) (else (A257803 (+ 1 (A260432 (/ (- n 1) 2)))))))

%Y Inverse: A260431.

%Y Related permutations: A260434, A260430, A054429.

%Y Cf. A257803, A257804, A257807, A257808.

%Y Cf. also A233271, A257806.

%K nonn,tabf

%O 1,2

%A _Antti Karttunen_, Jul 27 2015