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.

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, 117, 91, 1292, 22, 70, 38, 72, 680, 93, 111, 295, 1229, 16, 47, 26, 29, 102, 12, 20, 23, 58, 302, 73, 189, 147, 2090, 21, 34, 39, 35, 113, 44, 61, 116, 1100, 162, 150, 179, 477

Offset

0,3

Links

Table of n, a(n) for n=0..63.

A. Karttunen, Gatomorphisms

Index entries for sequences that are permutations of the natural numbers

Prog

(Scheme functions below show the essential idea. For a complete source, follow the "Gatomorphisms" link.)
(define A072656 (lexrank->arithrank-bijection packA048680oA054238))
(define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))
(define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
(define (packA048680oA054238tr x y) (A048680 (packA054238tr x y)))
(define (packA054238tr x y) (+ (A000695 y) (* 2 (A000695 x))))

Crossrefs

Inverse permutation: A072659. Cf. also A014486, A000695, A054238, A048680, A071651, A072634, A072636, A072646, A072656, A072660.

Sequence in context: A239965 A072767 A071651 * A099864 A292956 A056535

Adjacent sequences: A072655 A072656 A072657 * A072659 A072660 A072661

Keyword

nonn

Author

Antti Karttunen, Jun 02 2002

Status

approved