A075161 - OEIS

A075161

Position of A075165(n+1) in A014486.

0, 1, 2, 3, 4, 5, 9, 7, 6, 10, 23, 12, 65, 24, 11, 8, 197, 15, 626, 26, 25, 66, 2056, 13, 14, 198, 16, 68, 6918, 29, 23714, 17, 67, 627, 28, 40, 82500, 2057, 199, 27, 290512, 71, 1033412, 200, 30, 6919, 3707852, 31, 37, 38, 628, 629, 13402697, 43, 70, 69, 2058

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

See A075166.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..1024

A. Karttunen, Alternative Catalan Orderings (with the complete Scheme source)

Index entries for sequences that are permutations of the natural numbers

PROG

(Scheme functions showing the essential idea. For the complete source, follow the "Alternative Catalan Orderings" link:)

(define (A075161 n) (CatalanRankGlobal (parenthesization->binexp (primefactorization->parenthesization (1+ n)))))

(define (primefactorization->parenthesization n) (map primefactorization->parenthesization (explist->Nvector! (primefactorization->explist n))))

Function primefactorization->explist maps 1 to (), 2 to (1), 3 to (1 0), 4 to (2), 12 to (1 2), etc.

(define (explist->Nvector! el) (cond ((pair? el) (let loop ((el (cdr el))) (cond ((pair? el) (set-car! el (1+ (car el))) (loop (cdr el))))))) el)

CROSSREFS

Inverse of A075162. a(n) = A075163(n+1)-1. Cf. A075168.

Sequence in context: A346097 A346098 A245821 * A298268 A329044 A222251

Adjacent sequences: A075158 A075159 A075160 * A075162 A075163 A075164

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 13 2002

STATUS

approved