A082313 Involution of natural numbers: A057501-conjugate of A057164.

0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 21, 14, 18, 13, 11, 22, 16, 17, 12, 19, 20, 10, 15, 23, 58, 37, 49, 35, 28, 62, 42, 46, 32, 51, 55, 27, 41, 25, 59, 39, 50, 36, 30, 63, 44, 45, 31, 53, 54, 26, 40, 33, 64, 47, 48, 34, 56, 57, 24, 38, 60, 61, 29, 43, 52, 65, 170, 107, 142, 100

Offset

0,3

Comments

Note: This is isomorphic with Meeussen's "skewcatacycleft" operation acting on the interpretation (gg) of the exercise 19 by Stanley.

Links

Table of n, a(n) for n=0..69.

Index entries for signature-permutations induced by Catalan automorphisms

R. P. Stanley, Exercises on Catalan and Related Numbers

Formula

a(n) = A057501(A057164(A057502(n)))

Crossrefs

a(n) = A069888(A057502(n)). Occurs in A073200 as row 604463486276865131809167. Cf. also A082314, A082315, A082333, A082334.

Number of cycles: A007123. Number of fixed-points: A001405. Max. cycle size: A046698. LCM of cycle sizes: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Sequence in context: A123492 A123493 A123715 * A123494 A123716 A329717

Adjacent sequences: A082310 A082311 A082312 * A082314 A082315 A082316

Keyword

nonn

Author

Antti Karttunen, Apr 17 2003. Proposed by Wouter Meeussen in Dec 15 2001.

Status

approved