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A072635 Inverse permutation to A072634. 6
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 (list; graph; refs; listen; history; text; internal format)
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 A210754 A210738

Adjacent sequences:  A072632 A072633 A072634 * A072636 A072637 A072638

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2002

STATUS

approved

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Last modified January 15 19:06 EST 2019. Contains 319171 sequences. (Running on oeis4.)