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%I #6 May 01 2014 02:43:28
%S 0,1,3,2,6,8,7,19,16,5,15,4,14,52,43,51,42,20,22,53,60,21,61,56,179,
%T 155,178,154,177,164,557,163,556,11,39,13,41,151,123,153,125,12,40,33,
%U 117,152,124,471,381,477,553,479,555,505,1797,507,1799,478,554,1536
%N Inverse permutation to A072634.
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme functions below show the essential idea. For a complete source, follow the "Gatomorphisms" link.)
%o (define A072635 (arithrank->lexrank-bijection A059905 A059906))
%o (define (arithrank->lexrank-bijection pr1 pr2) (lambda (n) (CatalanRankGlobal (parenthesization->binexp (unrank-bintree n pr1 pr2)))))
%o (define (unrank-bintree rank pr1 pr2) (cond ((zero? rank) (list)) (else (cons (unrank-bintree (pr1 (-1+ rank)) pr1 pr2) (unrank-bintree (pr2 (-1+ rank)) pr1 pr2)))))
%o (define (A059905 n) (if (zero? n) n (+ (modulo n 2) (* 2 (A059905 (floor->exact (/ n 4)))))))
%o (define (A059906 n) (A059905 (floor->exact (/ n 2))))
%Y A072644 gives the size of the corresponding parenthesizations, i.e. A072644(n) = A029837(A014486(A072635(n))+1)/2 [A029837(n+1) gives the binary width of n].
%Y A072635(n) = A057163(A072637(n)). Cf. also A014486, A059905, A059906, A071652, A072647, A072637.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 02 2002