A072635 Inverse permutation to A072634.

0, 1, 3, 2, 6, 8, 7, 19, 16, 5, 15, 4, 14, 52, 43, 51, 42, 20, 22, 53, 60, 21, 61, 56, 179, 155, 178, 154, 177, 164, 557, 163, 556, 11, 39, 13, 41, 151, 123, 153, 125, 12, 40, 33, 117, 152, 124, 471, 381, 477, 553, 479, 555, 505, 1797, 507, 1799, 478, 554, 1536

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 A072635 (arithrank->lexrank-bijection A059905 A059906))
(define (arithrank->lexrank-bijection pr1 pr2) (lambda (n) (CatalanRankGlobal (parenthesization->binexp (unrank-bintree n pr1 pr2)))))
(define (unrank-bintree rank pr1 pr2) (cond ((zero? rank) (list)) (else (cons (unrank-bintree (pr1 (-1+ rank)) pr1 pr2) (unrank-bintree (pr2 (-1+ rank)) pr1 pr2)))))
(define (A059905 n) (if (zero? n) n (+ (modulo n 2) (* 2 (A059905 (floor->exact (/ n 4)))))))
(define (A059906 n) (A059905 (floor->exact (/ n 2))))

Crossrefs

A072644 gives the size of the corresponding parenthesizations, i.e. A072644(n) = A029837(A014486(A072635(n))+1)/2 [A029837(n+1) gives the binary width of n].

A072635(n) = A057163(A072637(n)). Cf. also A014486, A059905, A059906, A071652, A072647, A072637.

Sequence in context: A131161 A131006 A122362 * A318049 A352877 A210754

Adjacent sequences: A072632 A072633 A072634 * A072636 A072637 A072638

Keyword

nonn

Author

Antti Karttunen, Jun 02 2002

Status

approved