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A250243 Permutation of natural numbers: a(n) = A246275(A055396(n+1), a(A078898(n+1))).

%I A250243 #13 Nov 17 2014 22:03:01
%S A250243 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,26,21,22,23,24,25,20,
%T A250243 27,28,29,30,31,44,33,34,35,36,37,32,51,40,41,42,43,80,45,46,47,48,49,
%U A250243 74,39,52,53,124,55,62,57,58,59,60,61,38,87,54,65,66,67,134,69,70,71,72,73,50,63,76,101,78,79,98,81
%N A250243 Permutation of natural numbers: a(n) = A246275(A055396(n+1), a(A078898(n+1))).
%C A250243 This is a "more recursed" variant of A249816. Preserves the parity of n.
%H A250243 Antti Karttunen, <a href="/A250243/b250243.txt">Table of n, a(n) for n = 1..5749</a>
%H A250243 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A250243 a(n) = A246275(A055396(n+1), a(A078898(n+1))).
%F A250243 As a composition of other permutations:
%F A250243 a(n) = A246684(A249813(n)).
%F A250243 Other identities. For all n >= 1, the following holds:
%F A250243 a(n) = (1+a((2*n)-1))/2. [The odd bisection from a(1) onward with one added and then halved gives the sequence back.]
%F A250243 a(A006093(n)) = A006093(n). [Primes minus one are among the fixed points].
%o A250243 (Scheme, with memoization-macro definec from _Antti Karttunen_'s IntSeq-library)
%o A250243 (definec (A250243 n) (cond ((<= n 1) n) (else (+ -1 (A246278bi (A055396 (+ 1 n)) (A250243 (A078898 (+ 1 n)))))))) ;; Code for A246278bi given in A246278.
%Y A250243 Inverse: A250244.
%Y A250243 Cf. A006093, A055396, A078898, A246275, A246278.
%Y A250243 Similar or related permutations: A246684, A249813, A250246.
%Y A250243 Differs from A249815 and A250244 for the first time at n=32, where a(32) = 44, while A249815(32) = A250244(32) = 38.
%Y A250243 Differs from "shallow variant" A249816 for the first time at n=39, where a(39) = 51, while A249816(39) = 39.
%K A250243 nonn
%O A250243 1,2
%A A250243 _Antti Karttunen_, Nov 16 2014