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%I #9 Jul 27 2015 22:14:35
%S 1,2,4,3,8,6,5,16,9,12,10,7,32,18,24,20,17,13,14,64,11,36,33,19,25,48,
%T 21,40,34,15,26,28,128,65,37,22,72,49,66,38,41,35,50,96,42,80,68,30,
%U 27,52,56,29,129,23,73,256,67,130,74,39,44,144,98,51,97,132,76,43,82,81,70,100,69,31,53,57,257,192,84,160,131,75,45,136,60,54
%N Permutation of natural numbers: a(1) = 1, a(A257804(n)) = 2*a(n), a(A257803(1+n)) = 1 + 2*a(n), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.
%H Antti Karttunen, <a href="/A260431/b260431.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1; for n > 1, if A257800(n) = 0 [when n is one of the terms of A257804] a(n) = 2*a(A257808(n)), otherwise [when n is one of the terms of A257803] a(n) = 1 + 2*a(A257807(n)-1).
%F As a composition of other permutations:
%F a(n) = A054429(A260433(n)).
%F a(n) = A260433(A260430(n)).
%o (Scheme, with memoizing macro definec)
%o (definec (A260431 n) (cond ((<= n 1) n) ((zero? (A257800 n)) (* 2 (A260431 (A257808 n)))) (else (+ 1 (* 2 (A260431 (+ -1 (A257807 n))))))))
%Y Inverse: A260432.
%Y Related permutations: A260433, A260430, A054429.
%Y Cf. A257800, A257803, A257804, A257807, A257808, A233271.
%Y Cf. also A257806.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 27 2015
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