|
%I #15 Jan 14 2015 16:15:43
%S 1,2,4,3,8,5,6,16,9,7,10,12,32,17,11,13,18,14,20,24,33,19,64,15,21,25,
%T 34,22,26,36,28,40,65,35,23,27,48,37,29,41,66,38,128,30,42,49,50,68,
%U 67,44,39,52,72,129,31,43,51,69,56,45,80,53,130,73,57,70,46,54,81,96,74,58,82,131,132,76,71,256,60
%N Permutation of natural numbers: a(1) = 1; thereafter, if n is k-th number with an odd number of prime divisors (counted with multiplicity) [i.e., n = A026424(k)], a(n) = 2*a(k), otherwise, when n is k-th number > 1 with an even number of prime divisors [i.e., n = A028260(1+k)], a(n) = 1+(2*a(k)).
%H Antti Karttunen, <a href="/A245603/b245603.txt">Table of n, a(n) for n = 1..10001</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, and for n > 1, if A066829(n) = 1, then a(n) = 2 * A245603(A055038(n)), otherwise a(n) = 1 + (2 * A245603(A055037(n)-1)).
%F As a composition of related permutations:
%F a(n) = A244321(A245613(n)).
%F For all n >= 1, A000035(a(n)) = 1 - A066829(n). [Permutation A143692 has the same property.]
%o (Scheme, with memoization macro definec)
%o (definec (A245603 n) (cond ((= 1 n) 1) ((= 1 (A066829 n)) (* 2 (A245603 (A055038 n)))) (else (+ 1 (* 2 (A245603 (-1+ (A055037 n))))))))
%Y Inverse: A245604.
%Y Cf. A026424, A028260, A066829, A055037, A055038.
%Y Similar permutations: A143692, A244152, A244321, A245613, A245605, A245607.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 27 2014
|
