A079269 Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(1+1/b(n-1)); sequence gives numerator of b(n).

1, 3, 21, 861, 1275141, 2551762438701, 9546380157472159016030421, 126857284256055227389078067834858327568823447932861

Offset

1,2

Links

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

Leroy Quet, a(m) =a(m-1)+1/(1+1/a(m-1)), posting to SeqFan mailing list, Feb 15 2003.

Formula

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

Example

The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ... = a(n)/A079278.

Maple

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

Mathematica

nxt[n_]:=n+1/(1+1/n); Numerator/@Nest[Append[#, nxt[Last[#]]]&, {1}, 10]  (* Harvey P. Dale, Apr 21 2011 *)

Crossrefs

Cf. A079278, A080581, A080582, A080984, A080985.

Sequence in context: A171104 A057600 A162924 * A127104 A176430 A340505

Adjacent sequences: A079266 A079267 A079268 * A079270 A079271 A079272

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 16 2003

Extensions

The next term is too large to include.

Status

approved