A249813 Permutation of natural numbers: a(1) = 1, a(n) = A000079(A055396(n+1)-1) * ((2 * a(A078898(n+1))) - 1).

1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 15, 32, 13, 10, 11, 64, 17, 128, 31, 14, 29, 256, 63, 12, 25, 18, 19, 512, 21, 1024, 127, 30, 33, 20, 255, 2048, 61, 26, 27, 4096, 57, 8192, 511, 22, 125, 16384, 23, 24, 49, 34, 35, 32768, 37, 28, 1023, 62, 41, 65536, 2047, 131072, 253, 58, 59, 36, 65, 262144, 39, 126, 509, 524288, 4095, 1048576, 121, 50, 51, 40, 53

Offset

1,2

Comments

This sequence is a "recursed variant" of A249812.

See also the comments at the inverse permutation A249814.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1024

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(n) = A000079(A055396(n+1)-1) * ((2 * a(A078898(n+1))) - 1).

As a composition of other permutations:

a(n) = A246683(A250243(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)) = A000079(n-1).

Prog

(Scheme, with memoizing macro definec from Antti Karttunen's IntSeq-library)
(definec (A249813 n) (cond ((<= n 1) n) (else (* (A000079 (- (A055396 (+ 1 n)) 1)) (+ -1 (* 2 (A249813 (A078898 (+ 1 n)))))))))

Crossrefs

Inverse: A249814.

Similar or related permutations: A246683, A249812, A250243.

Cf. A000079, A006093, A055396, A078898.

Differs from A246683 for the first time at n=20, where a(20) = 14, while A246683(20) = 18.

Sequence in context: A246677 A156552 A269383 * A246683 A332816 A354732

Adjacent sequences: A249810 A249811 A249812 * A249814 A249815 A249816

Keyword

nonn

Author

Antti Karttunen, Nov 06 2014

Status

approved