A082341 Permutation of natural numbers induced by the Catalan bijection gma082341 acting on the parenthesizations encoded by A014486/A063171.

0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 12, 11, 13, 17, 18, 16, 14, 15, 20, 21, 19, 22, 23, 24, 26, 25, 27, 31, 32, 30, 28, 29, 34, 35, 33, 36, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 54, 55, 57, 58, 59, 53, 56, 51, 52, 61, 62, 63, 60, 64, 65, 66, 68, 67, 69

Offset

0,3

Comments

This is A057163-conjugate of A073285.

Links

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

A. Karttunen, Gatomorphisms (with the complete Scheme source)

Index entries for signature-permutations induced by Catalan automorphisms

Prog

(Scheme functions implementing this automorphism on list-structures:)
(define (gma082341! s) (cond ((pair? s) (gma082341! (car s)) (gma072797! s) (gma082341! (cdr s)))) s)

Crossrefs

Inverse of A082342. a(n) = A057163(A073285(A057163(n))). Occurs in A073200 as row 1800. Cf. also A072797, A082337-A082339.

Differs from A082326 first time at n=39: a(39)=48, while A082326(39)=49.

Number of cycles: A057513. Number of fixed-points: A057546. Max. cycle size: A000793. LCM of cycle sizes: A003418. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Sequence in context: A371960 A082339 A082340 * A130936 A082326 A082342

Adjacent sequences: A082338 A082339 A082340 * A082342 A082343 A082344

Keyword

nonn

Author

Antti Karttunen, Apr 17 2003

Status

approved