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.

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, 258, 4101, 4117, 22, 65, 69, 1030, 1090, 81, 1026, 16390, 16454, 20, 23, 19, 68, 72, 13, 14, 36, 521, 547, 42, 515, 8201, 8233, 15, 16, 34, 43, 129, 132, 137, 2059, 2179

Offset

0,3

Links

Table of n, a(n) for n=0..59.

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 A072636 (lexrank->arithrank-bijection packA054238tr))
(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 (packA054238tr x y) (+ (A000695 y) (* 2 (A000695 x))))

Crossrefs

Inverse permutation: A072637. Cf. also A014486, A000695, A054238, A071651, A072634, A072646, A072656, A072658, A072644.

Sequence in context: A195610 A342038 A082654 * A191741 A191665 A306233

Adjacent sequences: A072633 A072634 A072635 * A072637 A072638 A072639

Keyword

nonn

Author

Antti Karttunen, Jun 02 2002

Status

approved