%I A072636
%S A072636 0,1,2,3,5,6,4,9,11,18,21,17,66,70,7,8,10,35,41,12,33,131,139,261,274,
%T A072636 258,4101,4117,22,65,69,1030,1090,81,1026,16390,16454,20,23,19,68,72,
%U A072636 13,14,36,521,547,42,515,8201,8233,15,16,34,43,129,132,137,2059,2179
%N A072636 Permutation of natural numbers induced by reranking plane binary trees 
               given in the standard lexicographic order (A014486) with an "arithmetic 
               global ranking algorithm", using packA054238tr as the packing bijection 
               N X N -> N.
%H A072636 A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/
               gatomorf.htm">Gatomorphisms</a>
%H A072636 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%o A072636 (Scheme functions below show the essential idea. For a complete source, 
               follow the "Gatomorphisms" link.)
%o A072636 (define A072636 (lexrank->arithrank-bijection packA054238tr))
%o A072636 (define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree 
               (binexp->parenthesization (A014486 n)) packfun)))
%o A072636 (define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ 
               (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
%o A072636 (define (packA054238tr x y) (+ (A000695 y) (* 2 (A000695 x))))
%Y A072636 Inverse permutation: A072637. Cf. also A014486, A000695, A054238, A071651, 
               A072634, A072646, A072656, A072658, A072644.
%Y A072636 Sequence in context: A137760 A054077 A082654 this_sequence A001600 A000036 
               A165081
%Y A072636 Adjacent sequences: A072633 A072634 A072635 this_sequence A072637 A072638 
               A072639
%K A072636 nonn
%O A072636 0,3
%A A072636 Antti Karttunen Jun 02 2002