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

1,2

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

References

Suggested by Leroy Quet, Feb 14 2003.

Links

Table of n, a(n) for n=1..8.

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.

Example

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

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 *)

Crossrefs

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

Cf. A080581, A080582.

Sequence in context: A321267 A111837 A092123 * A275611 A015178 A296178

Adjacent sequences: A079275 A079276 A079277 * A079279 A079280 A079281

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 16 2003

Status

approved