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A250250 Permutation of natural numbers: a(1) = 1, a(n) = A246278(a(A055396(n)),a(A078898(n))).

%I A250250 #8 Nov 19 2014 00:05:01
%S A250250 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,27,22,23,24,25,26,
%T A250250 21,28,29,30,31,32,45,34,35,36,37,38,33,40,41,54,43,44,81,46,47,48,49,
%U A250250 50,75,52,53,42,125,56,63,58,59,60,61,62,39,64,55,90,67,68,135,70,71,72,103,74,51,76,77,66,79,80,99,82,83
%N A250250 Permutation of natural numbers: a(1) = 1, a(n) = A246278(a(A055396(n)),a(A078898(n))).
%C A250250 This is a "doubly-recursed" version of A249818.
%H A250250 Antti Karttunen, <a href="/A250250/b250250.txt">Table of n, a(n) for n = 1..3432</a>
%H A250250 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A250250 a(1) = 1, a(n) = A246278(a(A055396(n)), a(A078898(n))).
%F A250250 Other identities. For all n >= 1:
%F A250250 a(2n) = 2*a(n), or equally, a(n) = a(2n)/2. [The even bisection halved gives the sequence back].
%F A250250 a(p_n) = p_{a(n)}, or equally, a(n) = A049084(a(A000040(n))). [Restriction to primes induces the same sequence].
%F A250250 A078442(a(n)) = A078442(n), A049076(a(n)) = A049076(n). [Preserves the "order of primeness of n"].
%F A250250 A000035(n) = A000035(a(n)). [Preserves the parity].
%o A250250 (Scheme, with memoizing-macro definec from _Antti Karttunen_'s IntSeq-library)
%o A250250 (definec (A250250 n) (cond ((<= n 1) n) (else (A246278bi (A250250 (A055396 n)) (A250250 (A078898 n)))))) ;; Code for A246278bi given in A246278
%Y A250250 Inverse: A250249.
%Y A250250 Fixed points: A250251, their complement: A249729.
%Y A250250 Cf. A000035, A000040, A055396, A078442, A078898, A049076, A246278.
%Y A250250 See also other (somewhat) similar permutations: A245821, A057505.
%Y A250250 Differs from the "vanilla version" A249818 for the first time at n=42, where a(42) = 54, while A249818(42) = 42.
%K A250250 nonn
%O A250250 1,2
%A A250250 _Antti Karttunen_, Nov 17 2014