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

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, 27, 28, 29, 30, 31, 44, 33, 34, 35, 36, 37, 32, 51, 40, 41, 42, 43, 80, 45, 46, 47, 48, 49, 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

Offset

1,2

Comments

This is a "more recursed" variant of A249816. Preserves the parity of n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..5749

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A246275(A055396(n+1), a(A078898(n+1))).

As a composition of other permutations:

a(n) = A246684(A249813(n)).

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

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.]

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

Prog

(Scheme, with memoization-macro definec from Antti Karttunen's IntSeq-library)
(definec (A250243 n) (cond ((<= n 1) n) (else (+ -1 (A246278bi (A055396 (+ 1 n)) (A250243 (A078898 (+ 1 n)))))))) ;; Code for A246278bi given in A246278.

Crossrefs

Inverse: A250244.

Cf. A006093, A055396, A078898, A246275, A246278.

Similar or related permutations: A246684, A249813, A250246.

Differs from A249815 and A250244 for the first time at n=32, where a(32) = 44, while A249815(32) = A250244(32) = 38.

Differs from "shallow variant" A249816 for the first time at n=39, where a(39) = 51, while A249816(39) = 39.

Sequence in context: A249815 A250244 A249816 * A341936 A066566 A256577

Adjacent sequences: A250240 A250241 A250242 * A250244 A250245 A250246

Keyword

nonn

Author

Antti Karttunen, Nov 16 2014

Status

approved