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A250245 Permutation of natural numbers: a(1) = 1, a(n) = A083221(A055396(n),a(A246277(n))).

%I A250245 #22 Jan 18 2015 19:04:32
%S A250245 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 A250245 21,28,29,30,31,32,39,34,35,36,37,38,63,40,41,54,43,44,33,46,47,48,49,
%U A250245 50,75,52,53,42,65,56,99,58,59,60,61,62,57,64,95,78,67,68,111,70,71,72,73,74,51,76,77,126,79,80,45,82
%N A250245 Permutation of natural numbers: a(1) = 1, a(n) = A083221(A055396(n),a(A246277(n))).
%C A250245 The first 7-cycle occurs at: (33 39 63 57 99 81 45) which is mirrored by the cycle (66 78 126 114 198 162 90) with double-size terms.
%C A250245 The cycle which contains 55 as its smallest term, goes as: 55, 65, 95, 185, 425, 325, 205, 455, 395, 1055, 2945, 6035, 30845, ...
%C A250245 while to the other direction (A250246) it goes as: 55, 125, 245, 115, 625, 8575, 40375, ...
%C A250245 The cycle which contains 69 as its smallest term, goes as: 69, 111, 183, 351, 261, 273, 387, 489, 939, 1863, 909, 1161, 981, 1281, 4167, ...
%C A250245 while to the other direction (A250246) it goes as: 69, 135, 87, 105, 225, 207, 231, 195, 525, 1053, 3159, 24909, ...
%H A250245 Antti Karttunen, <a href="/A250245/b250245.txt">Table of n, a(n) for n = 1..8192</a>
%H A250245 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A250245 a(1) = 1, a(n) = A083221(A055396(n), a(A246277(n))).
%F A250245 a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(a(A064989(2n+1))). - _Antti Karttunen_, Jan 18 2015
%F A250245 As a composition of related permutations:
%F A250245 a(n) = A252755(A243071(n)).
%F A250245 Other identities. For all n >= 1:
%F A250245 a(n) = a(2n)/2. [The even bisection halved gives the sequence back.]
%F A250245 A020639(a(n)) = A020639(n) and A055396(a(n)) = A055396(n). [Preserves the smallest prime factor of n].
%o A250245 (Scheme, with memoizing-macro definec from _Antti Karttunen_'s IntSeq-library, three alternative definitions)
%o A250245 (definec (A250245 n) (cond ((<= n 1) n) (else (A083221bi (A055396 n) (A250245 (A246277 n)))))) ;; Code for A083221bi given in A083221
%o A250245 (definec (A250245 n) (cond ((<= n 1) n) ((even? n) (* 2 (A250245 (/ n 2)))) (else (A250469 (A250245 (A064989 n))))))
%o A250245 (define (A250245 n) (A252755 (A243071 n)))
%Y A250245 Inverse: A250246.
%Y A250245 Other similar permutations: A250244, A250247, A250249, A243071, A252755.
%Y A250245 Cf. A005843, A020639, A055396, A064989, A083221, A246277, A250469.
%Y A250245 Differs from the "vanilla version" A249817 for the first time at n=42, where a(42) = 54, while A249817(42) = 42.
%Y A250245 Differs from A250246 for the first time at n = 33, where a(33) = 39, while A250246(33) = 45.
%Y A250245 Differs from A250249 for the first time at n=73, where a(73) = 73, while A250249(73) = 103.
%K A250245 nonn
%O A250245 1,2
%A A250245 _Antti Karttunen_, Nov 17 2014