|
%I #14 Jul 28 2015 05:37:36
%S 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 27,16,24,14,17,8,172,125,118,85,128,89,76,51,119,86,75,50,64,43,38,
%U 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 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 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 |
%C ...................1...................
%C 4 2
%C 12......../ \........6 7......../ \........3
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 30 19 18 10 21 11 9 5
%C 74 48 52 32 49 31 25 15 54 36 27 16 24 14 17 8
%C etc.
%C Note how this is a mirror image of the tree shown in A260432.
%H Antti Karttunen, <a href="/A260434/b260434.txt">Table of n, a(n) for n = 1..16383</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) = A257803(1+a(n)), a(2n+1) = A257804(a(n)).
%F As a composition of other permutations:
%F a(n) = A260432(A054429(n)).
%F a(n) = A260430(A260432(n)).
%o (Scheme, with memoizing macro definec)
%o (definec (A260434 n) (cond ((<= n 1) n) ((even? n) (A257803 (+ 1 (A260434 (/ n 2))))) (else (A257804 (A260434 (/ (- n 1) 2))))))
%Y Inverse: A260433.
%Y Related permutations: A260432, A260430, A054429.
%Y Cf. A257803, A257804, A257807, A257808.
%Y Cf. also A233271, A257806.
%K nonn,tabf,look
%O 1,2
%A _Antti Karttunen_, Jul 27 2015
|
