A080984 Define b by b(1) = 1 and for n > 1, b(n) = b(n-1) + 1/(2 + 1/b(n-1)); sequence gives numerator of b(n).

1, 4, 56, 9968, 294115808, 242590126064151488, 158248601344912132157178428071499648, 65129411362626329768830076910903417752818896343320137665280356705971968

Offset

1,2

Comments

The next term has 285 digits. - Harvey P. Dale, Jul 07 2011

Links

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

Leroy Quet, Sequence & Its Numerators & Denominators, posting to SeqFan mailing list, Feb 26 2003.

Formula

b(k) = n(k)/d(k); n(1)=1, d(1)=1, m=2; for k >= 2: n(k+1) = n(k) *(m*n(k) + 2*d(k)), d(k+1) = d(k)*(m*n(k) + d(k)). - Leroy Quet

Example

The sequence {b(n)} begins 1, 4/3, 56/33, 9968/4785, 294115808/118289985, ...

Mathematica

Numerator/@NestList[#+1/(2+1/#)&, 1, 9] (* Harvey P. Dale, Jul 07 2011 *)

Prog

(Reduce) a := 1; for i := 1:8 do write a := a+1/(2+1/a);

Crossrefs

Cf. A080985, A080986, A080987, A079269, A079278.

Sequence in context: A070019 A056075 A000315 * A071579 A060497 A092273

Adjacent sequences: A080981 A080982 A080983 * A080985 A080986 A080987

Keyword

frac,nonn

Author

Hugo Pfoertner, Feb 26 2003

Status

approved