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A250247 Permutation of natural numbers: a(1) = 1, a(n) = A083221(a(A055396(n)),A246277(n)).

%I A250247 #12 Nov 19 2014 00:04:39
%S A250247 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 A250247 21,28,29,30,31,32,39,34,35,36,37,38,63,40,41,42,43,44,33,46,47,48,49,
%U A250247 50,75,52,53,54,65,56,99,58,59,60,61,62,57,64,95,66,67,68,111,70,71,72,103,74,51,76,77,78,79,80,45,82
%N A250247 Permutation of natural numbers: a(1) = 1, a(n) = A083221(a(A055396(n)),A246277(n)).
%C A250247 The first 7-cycle occurs at: (33 39 63 57 99 81 45), which is mirrored at the cycle (137 167 307 269 523 419 197), consisting of primes (p_33, p_39, p_63, ...).
%H A250247 Antti Karttunen, <a href="/A250247/b250247.txt">Table of n, a(n) for n = 1..4240</a>
%H A250247 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A250247 a(1) = 1, a(n) = A083221(a(A055396(n)),A246277(n)).
%F A250247 Other identities. For all n >= 1:
%F A250247 a(A005843(n)) = A005843(n). [Fixes even numbers].
%F A250247 a(p_n) = p_{a(n)}, or equally, a(n) = A049084(a(A000040(n))). [Restriction to primes induces the same sequence].
%F A250247 A078442(a(n)) = A078442(n), A049076(a(n)) = A049076(n). [Preserves the "order of primeness of n"].
%e A250247 As a(21) = 27, and A000040(21) = 73 and A000040(27) = 103, a(73) = 103.
%o A250247 (Scheme, with memoizing-macro definec from _Antti Karttunen_'s IntSeq-library)
%o A250247 (definec (A250247 n) (cond ((<= n 1) n) (else (A083221bi (A250247 (A055396 n)) (A246277 n))))) ;; Code for A083221bi given in A083221
%Y A250247 Inverse: A250248.
%Y A250247 Cf. A000040, A005843, A049076, A049084, A055396, A078442, A083221, A246277.
%Y A250247 Differs from its inverse A250248 for the first time at n = 33, where a(33) = 39, while A250248(33) = 45.
%Y A250247 Differs from the "vanilla version" A249817 for the first time at n=73, where a(73) = 103, while A249817(73) = 73.
%Y A250247 Differs from "doubly recursed" version A250249 for the first time at n=42, where a(42) = 42, while A250249(42) = 54, thus the first prime where they get different values is p_42 = 181, where a(181) = 181, while A250249(181) = 251 = p_54.
%K A250247 nonn
%O A250247 1,2
%A A250247 _Antti Karttunen_, Nov 17 2014