A066932 a(n) is the denominator of b(n) where b(n)=1/b(n-1)+1/b(n-2) with b(1)=1 and b(2)=2.

1, 1, 2, 6, 21, 224, 10848, 4843293, 98262557120, 989063619297120960, 197348115975871052843094930213, 380244324677612882673067751880150651746235378560

Offset

1,3

Comments

Limit_{n->oo} b(n)=sqrt(2) with geometric convergence since abs(b(n)-sqrt(2))<2*2^(-n/2)

Links

Table of n, a(n) for n=1..12.

Formula

a(n+1) = A057677(n)*A057677(n-1). - Benoit Cloitre, Oct 25 2005

a(n) is the numerator of c(n) where c(n)=1/(c(n-1)+c(n-2)) with c(0)=c(1)=1. - Mark Dols, Jul 17 2009

Mathematica

nxt[{a_, b_}]:={b, 1/a+1/b}; NestList[nxt, {1, 2}, 20][[;; , 1]]//Denominator (* Harvey P. Dale, Apr 02 2024 *)

Crossrefs

Cf. A057677 (numerator), A074937, A162924, A162926.

Sequence in context: A110306 A351691 A028936 * A181754 A367678 A368005

Adjacent sequences: A066929 A066930 A066931 * A066933 A066934 A066935

Keyword

nonn,frac

Author

Zak Seidov, Oct 24 2002

Extensions

Edited by Benoit Cloitre, Oct 25 2005

Status

approved