cp's OEIS Frontend

A072658 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA048680oA054238tr as the packing bijection N X N -> N.

%I A072658 #5 May 01 2014 02:43:29
%S A072658 0,1,2,3,4,7,5,6,11,9,28,15,17,62,8,13,10,14,45,18,24,27,100,36,187,
%T A072658 117,91,1292,22,70,38,72,680,93,111,295,1229,16,47,26,29,102,12,20,23,
%U A072658 58,302,73,189,147,2090,21,34,39,35,113,44,61,116,1100,162,150,179,477
%N A072658 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA048680oA054238tr as the packing bijection N X N -> N.
%H A072658 A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a>
%H A072658 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A072658 (Scheme functions below show the essential idea. For a complete source, follow the "Gatomorphisms" link.)
%o A072658 (define A072656 (lexrank->arithrank-bijection packA048680oA054238))
%o A072658 (define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))
%o A072658 (define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
%o A072658 (define (packA048680oA054238tr x y) (A048680 (packA054238tr x y)))
%o A072658 (define (packA054238tr x y) (+ (A000695 y) (* 2 (A000695 x))))
%Y A072658 Inverse permutation: A072659. Cf. also A014486, A000695, A054238, A048680, A071651, A072634, A072636, A072646, A072656, A072660.
%K A072658 nonn
%O A072658 0,3
%A A072658 _Antti Karttunen_, Jun 02 2002