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A120705
Permutation of natural numbers induced by the Catalan bijection gma120705 acting on the binary trees encoded by A014486/A063171.
10
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.)
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 28 2006
STATUS
approved