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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). 2
1, 4, 56, 9968, 294115808, 242590126064151488, 158248601344912132157178428071499648, 65129411362626329768830076910903417752818896343320137665280356705971968 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Suggested by Leroy Quet, Feb 26 2003.

The next term has 285 digits. [From Harvey P. Dale, Jul 07 2011]

LINKS

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

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 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

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Last modified June 23 16:45 EDT 2017. Contains 288666 sequences.