A079278 Define a rational sequence {b(n)} as b(1) = 1, b(n) = b(n-1) + 1/(1 + 1/b(n-1)) for n > 1; a(n) is the denominator of b(n).

1, 2, 10, 310, 363010, 594665194510, 1871071000515058250871610, 21362861761506953021644584296874581450310229239910

Offset: 1

Author

N. J. A. Sloane, Feb 16 2003

Keywords

• nonn
• frac

Comments

The next term is too large to include.

The same sequence of denominators is produced by c(1) = 1 and for n > 1, c(n) = c(n-1) + 1/(n + 1 - c(n-1)). In that case, the sequence begins 1, 3/2, 19/10, 689/310, 902919/363010, 1610893922869/594665194510, ... . - Leonid Broukhis, Jul 09 2022

Examples

			The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ...
		

References

• Suggested by Leroy Quet, Feb 14 2003.

Crossrefs

Cf. A079269 (numerators), A355615 (other numerators).

Cf. A080581, A080582.

Programs

Maple

b := proc(n) option remember; if n=1 then 1 else b(n-1)+1/(1+1/b(n-1)); fi; end;

Mathematica

Denominator[NestList[#+1/(1+1/#)&,1,10]] (* Harvey P. Dale, Oct 07 2012 *)

Formula

Conjecture (Quet): a(m+1) = a(m)^2 + a(m)^3 / a(m-1)^2 - a(m)*a(m-1)^2 for m >= 2.