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Permutation of natural numbers: a(1) = 1, a(n) = A246278(a(A055396(n)),A078898(n)).
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%I #7 Nov 19 2014 00:04:47

%S 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 21,28,29,30,31,32,45,34,35,36,37,38,33,40,41,42,43,44,81,46,47,48,49,

%U 50,75,52,53,54,125,56,63,58,59,60,61,62,39,64,55,66,67,68,135,70,71,72,103,74,51,76,77,78,79,80,99,82,83

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

%H Antti Karttunen, <a href="/A250248/b250248.txt">Table of n, a(n) for n = 1..3432</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(1) = 1, a(n) = A246278(a(A055396(n)), A078898(n)).

%F Other identities. For all n >= 1:

%F a(A005843(n)) = A005843(n). [Fixes even numbers].

%F a(p_n) = p_{a(n)}, or equally, a(n) = A049084(a(A000040(n))). [Restriction to primes induces the same sequence].

%F A078442(a(n)) = A078442(n), A049076(a(n)) = A049076(n). [Preserves the "order of primeness of n"].

%o (Scheme, with memoizing-macro definec from _Antti Karttunen_'s IntSeq-library)

%o (definec (A250248 n) (cond ((<= n 1) n) (else (A246278bi (A250248 (A055396 n)) (A078898 n))))) ;; Code for A246278bi given in A246278

%Y Inverse: A250247.

%Y Similar permutations: A250250 for even more recursed variant of A249818.

%Y Cf. A000040, A005843, A049076, A049084, A055396, A078442, A078898, A246278.

%Y Differs from the "vanilla version" A249818 for the first time at n=73, where a(73) = 108, while A249818(73) = 73.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 17 2014