A120705 Permutation of natural numbers induced by the Catalan bijection gma120705 acting on the binary trees encoded by A014486/A063171.

0, 1, 3, 2, 8, 7, 4, 5, 6, 22, 21, 17, 18, 20, 10, 9, 11, 13, 12, 14, 15, 19, 16, 64, 63, 58, 59, 62, 46, 45, 48, 50, 49, 54, 55, 61, 57, 27, 26, 23, 24, 25, 29, 28, 33, 34, 35, 30, 36, 32, 31, 38, 37, 39, 41, 40, 51, 52, 60, 56, 42, 43, 44, 47, 53, 196, 195, 189, 190, 194

Offset

0,3

Comments

When the automorphisms A120705/A120705 act on the full Stern-Brocot tree (A007305/A047679), which is an infinite binary tree, they will move each fraction r to the position of 2*r (or r/2 respectively). See comments at A065249 and A065251. (Proof in preparation, to be published.)

Links

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

A. Karttunen, Gatomorphisms <I>(With the complete Scheme source)</I>

N. J. A. Sloane, Stern-Brocot or Farey Tree

Index entries for signature-permutations induced by Catalan automorphisms

Prog

(Scheme function implementing this automorphism on list-structures:)
(define (gma120705! s) (cond ((pair? s) (gma074680! s) (gma120705! (car s)) (cond ((pair? (cdr s)) (gma120705! (cddr s)) (gma120706! (cadr s)))))) s)

Crossrefs

Inverse of A120706. Cf. A074680.

Number of cycles: A120707. Number of fixed-points: A019590. Max. cycle size: A120708. LCM of cycle sizes: A120709.

Sequence in context: A074689 A122331 A074686 * A122296 A122359 A131007

Adjacent sequences: A120702 A120703 A120704 * A120706 A120707 A120708

Keyword

nonn

Author

Antti Karttunen, Jun 28 2006

Status

approved