|
| |
|
|
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).
|
|
2
| |
|
|
1, 5, 115, 57155, 13457544835, 718532108172999980195, 1987460976488531436231264449305834729789315, 14835338180729281137836887250133924105479472089418750626398379615457041439472496214755
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Suggested by Leroy Quet Feb 26 2003.
|
|
|
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, ...
|
|
|
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: A091026 A089638 A109057 * A156514 A006221 A144998
Adjacent sequences: A080985 A080986 A080987 * A080989 A080990 A080991
|
|
|
KEYWORD
| frac,nonn
|
|
|
AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 26 2003
|
| |
|
|
