%I #5 Mar 31 2012 13:21:14
%S 0,1,3,2,8,7,6,5,4,22,21,20,18,17,14,15,19,13,12,16,11,10,9,64,63,62,
%T 59,58,54,55,61,50,49,57,48,46,45,37,38,39,41,40,51,52,60,36,35,56,34,
%U 32,31,42,43,53,28,29,47,33,27,26,44,30,25,24,23,196,195,194,190,189
%N Signature-permutation of a Catalan automorphism, a self-inverse variant of A127377.
%C Used to construct A127388.
%H A. Karttunen, <a href="/A127387/b127387.txt">Table of n, a(n) for n = 0..2055</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o (Scheme implementation of this automorphism, destructive, that acts on S-expressions, i.e. list-structures:)
%o (define (*A127387! s) (cond ((null? s)) ((null? (car s)) (*A069770! s) (*A127387! (car s))) ((null? (cdr s)) (*A069770! s) (*A127387! (cdr s))) (else (*A127388! s))) s)
%Y The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this involution are given by A127385 and A127389. (This automorphism has the same fixed points as A127377/A127378). A127302(a(n)) = A127302(n) holds for all n.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007
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