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%I #7 Oct 15 2015 10:55:25
%S 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,
%T 59,62,46,45,48,50,49,54,55,61,57,27,26,23,24,25,29,28,33,34,35,30,36,
%U 32,31,38,37,39,41,40,51,52,60,56,42,43,44,47,53,196,195,189,190,194
%N Permutation of natural numbers induced by the Catalan bijection gma120705 acting on the binary trees encoded by A014486/A063171.
%C 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.)
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> <I>(With the complete Scheme source)</I>
%H N. J. A. Sloane, <a href="/stern_brocot.html">Stern-Brocot or Farey Tree</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>
%o (Scheme function implementing this automorphism on list-structures:)
%o (define (gma120705! s) (cond ((pair? s) (gma074680! s) (gma120705! (car s)) (cond ((pair? (cdr s)) (gma120705! (cddr s)) (gma120706! (cadr s)))))) s)
%Y Inverse of A120706. Cf. A074680.
%Y Number of cycles: A120707. Number of fixed-points: A019590. Max. cycle size: A120708. LCM of cycle sizes: A120709.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 28 2006
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