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

Author

Hugo Pfoertner, Feb 26 2003

Keywords

• frac
• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

Reduce

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

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