A072658 - OEIS

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

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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))))))