A250244 Permutation of natural numbers: a(n) = A249741(A055396(n+1), a(A246277(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, 38, 33, 34, 35, 36, 37, 62, 51, 40, 41, 42, 43, 32, 45, 46, 47, 48, 49, 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

Offset

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

Formula

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

As a composition of other permutations:

a(n) = A249814(A246683(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 (A250244 n) (cond ((<= n 1) n) (else (+ -1 (A083221bi (A055396 (+ 1 n)) (A250244 (A246277 (+ 1 n)))))))) ;; Code for A083221bi given in A083221.

Crossrefs

Inverse: A250243.

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

Similar or related permutations: A246683, A249814, A250245.

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

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

Sequence in context: A326872 A110548 A249815 * A249816 A250243 A341936

Adjacent sequences: A250241 A250242 A250243 * A250245 A250246 A250247

Keyword

nonn

Author

Antti Karttunen, Nov 16 2014

Status

approved