A071654 - OEIS

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A071654

Inverse permutation to A071653.

0, 1, 3, 2, 8, 6, 5, 7, 19, 15, 4, 22, 16, 52, 14, 13, 20, 60, 43, 51, 41, 11, 18, 53, 178, 42, 153, 39, 10, 21, 47, 155, 177, 125, 151, 38, 12, 61, 56, 136, 154, 555, 123, 150, 40, 33, 55, 179, 164, 135, 479, 553, 122, 152, 117, 29, 17, 159, 557, 163, 417, 477, 552, 124 (list; table; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	LINKS	`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 arithrankA001477->lexrank (arithrank->lexrank-bijection A025581 A002262))` `(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 (A002262 n) (- n (binomial_n_2 (floor->exact (+ (/ 1 2) (sqrt (* 2 (1+ n))))))))` `(define (A025581 n) (- (binomial_n_2 (1+ (floor->exact (+ (/ 1 2) (sqrt (* 2 (1+ n))))))) (1+ n)))`
	CROSSREFS	`Inverse permutation: A071653. A071672 gives the corresponding parenthesizations (from the term 1 onward) encoded as binary numbers, i.e. A071672(n) = A063171(A071654(n)) for n >= 1.` `a(n) = A057163(A071652(n)). Cf. also A014486, A002262, A025581, A071651, A071652.` `Sequence in context: A132827 A126315 A125976 * A072657 A098163 A072112` `Adjacent sequences: A071651 A071652 A071653 * A071655 A071656 A071657`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Antti Karttunen May 30 2002`

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Last modified February 15 20:26 EST 2012. Contains 205852 sequences.