A127289 Signature-permutation of a Catalan automorphism: composition of A127291 and A057164.

0, 1, 3, 2, 6, 8, 7, 5, 4, 15, 20, 14, 19, 21, 18, 22, 16, 11, 13, 17, 12, 10, 9, 39, 53, 41, 55, 59, 40, 54, 38, 52, 57, 37, 51, 56, 58, 47, 60, 49, 62, 64, 48, 61, 43, 29, 34, 42, 28, 33, 35, 50, 63, 46, 32, 36, 44, 30, 25, 27, 45, 31, 26, 24, 23, 113, 155, 118, 160, 173

Offset: 0

Author

Antti Karttunen, Jan 16 2007

Keywords

• nonn

Comments

This is otherwise like A127291, but uses A127285 instead of A127287 as a "picker permutation" for the function "tau", which can be found in the entry A127291. A014486->parenthesization is given in A014486. This permutation contains some exceptionally large cycles, see A127297.

Links

• A. Karttunen, Table of n, a(n) for n = 0..2055
• Index entries for signature-permutations of Catalan automorphisms

Crossrefs

Inverse: A127290. a(n) = A127291(A057164(n)) = A057164(A127299(n)). The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127296, A127297 and A127298.

Programs

Scheme

(define (A127289 n) (tau (A014486->parenthesization (A014486 n)) *A127285!))