A080988 Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(3+1/b(n-1)); sequence gives numerator of b(n).

1, 5, 115, 57155, 13457544835, 718532108172999980195, 1987460976488531436231264449305834729789315, 14835338180729281137836887250133924105479472089418750626398379615457041439472496214755

Offset

1,2

Comments

Suggested by Leroy Quet, Feb 26 2003.

Links

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

Formula

b[k]=n[k]/d[k]; n[1]=1, d[1]=1, m=3; for k>=2: n[k+1] = n[k] *(m*n[k] + 2*d[k]), d[k+1] = d[k] *(m*n[k] + d[k])

Example

The sequence begins 1, 5/4, 115/76, 57155/31996, 13457544835/6509938156, ...

Mathematica

NestList[#+1/(3+1/#)&, 1, 10]//Numerator (* Harvey P. Dale, Dec 13 2018 *)

Prog

Reduce: a := 1; for i := 1:8 do write a := a+1/(3+1/a);

Crossrefs

Cf. A080989, A080990, A080991, A079269, A079278.

Sequence in context: A255884 A109057 A245105 * A230338 A156514 A319392

Adjacent sequences: A080985 A080986 A080987 * A080989 A080990 A080991

Keyword

frac,nonn

Author

Hugo Pfoertner, Feb 26 2003

Status

approved