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%I #8 Oct 15 2015 10:55:24
%S 0,1,3,2,5,8,7,4,6,10,13,15,18,22,12,21,17,9,11,20,14,16,19,24,27,29,
%T 32,36,38,41,43,46,50,52,55,59,64,26,35,40,49,63,31,58,45,23,25,48,28,
%U 30,33,34,62,54,37,39,57,42,44,47,61,51,53,56,60,66,69,71,74,78
%N Permutation of natural numbers induced by the Catalan bijection gma085167 acting on symbolless S-expressions encoded by A014486/A063171.
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (With the complete Scheme source)
%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 (gma085167! s) (cond ((null? s) s) (else (app-to-xrt! (cdr s) (append! (car s) (list (list)))))))
%Y Inverse: A085168. a(n) = A085159(A069770(n)). Occurs in A073200. Cf. also A074679, A074680, A085203.
%Y Number of cycles in range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right: A001683. [To be checked.].
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 23 2003
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