A250244 - OEIS

%I #13 Nov 19 2014 00:04:06

%S 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 27,28,29,30,31,38,33,34,35,36,37,62,51,40,41,42,43,32,45,46,47,48,49,

%U 74,39,52,53,64,55,98,57,58,59,60,61,56,75,94,65,66,67,110,69,70,71,72,73,50,123,76,101,78,79,44,81,82,83,154,85,134,63,88,89

%N Permutation of natural numbers: a(n) = A249741(A055396(n+1), a(A246277(n+1))).

%C This is a "more recursed" variant of A249815. Preserves the parity of n.

%H Antti Karttunen, <a href="/A250244/b250244.txt">Table of n, a(n) for n = 1..8192</a>

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

%F a(n) = A249741(A055396(n+1), a(A246277(n+1))).

%F As a composition of other permutations:

%F a(n) = A249814(A246683(n)).

%F Other identities. For all n >= 1, the following holds:

%F 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 a(A006093(n)) = A006093(n). [Primes minus one are among the fixed points].

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

%o (definec (A250244 n) (cond ((<= n 1) n) (else (+ -1 (A083221bi (A055396 (+ 1 n)) (A250244 (A246277 (+ 1 n)))))))) ;; Code for A083221bi given in A083221.

%Y Inverse: A250243.

%Y Cf. A006093, A055396, A083221, A246277, A249741.

%Y Similar or related permutations: A246683, A249814, A250245.

%Y Differs from A249816 and A250243 for the first time at n=32, where a(32) = 38, while A249816(32) = A250243(32) = 44.

%Y Differs from the "shallow variant" A249815 for the first time at n=39, where a(39) = 51, while A249815(39) = 39

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 16 2014