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A080984
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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).
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2
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1, 4, 56, 9968, 294115808, 242590126064151488, 158248601344912132157178428071499648, 65129411362626329768830076910903417752818896343320137665280356705971968
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Suggested by Leroy Quet Feb 26 2003.
The next term has 285 digits. [From Harvey P. Dale, Jul 07 2011]
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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)
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EXAMPLE
| The sequence begins 1, 4/3, 56/33, 9968/4785, 294115808/118289985, ...
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MATHEMATICA
| Numerator/@NestList[#+1/(2+1/#)&, 1, 9] (* From Harvey P. Dale, Jul 07 2011 *)
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PROG
| Reduce: a := 1; for i := 1:8 do write a := a+1/(2+1/a);
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CROSSREFS
| Cf. A080985, A080986, A080987, A079269, A079278.
Sequence in context: A070019 A056075 A000315 * A071579 A060497 A092273
Adjacent sequences: A080981 A080982 A080983 * A080985 A080986 A080987
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KEYWORD
| frac,nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 26 2003
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