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A070986 Number of terms in simple continued fraction for sum(k=1,n,1/k^3). 0
1, 2, 5, 9, 14, 10, 15, 16, 14, 20, 22, 19, 33, 25, 27, 31, 41, 33, 52, 47, 36, 54, 38, 56, 50, 56, 65, 68, 81, 76, 77, 84, 75, 80, 88, 76, 90, 89, 98, 89, 113, 100, 110, 101, 104, 103, 121, 122, 131, 121, 131, 127, 124, 134, 127, 132, 143, 131, 143, 144, 161, 141 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sum(k>=1,1/k^3)=zeta(3)=1,2020...

LINKS

Table of n, a(n) for n=1..62.

FORMULA

lim n ->infinity a(n)/n=C=2, 5....

EXAMPLE

The simple continued fraction for sum(k=1,10,1/k^3) is [1, 5, 16, 135, 1, 5, 2, 3, 2, 1, 1, 1, 3, 3, 16, 1, 2, 1, 1, 2] which contains 20 terms, hence a(10)=20.

PROG

(PARI) for(n=1, 100, print1(length(contfrac(sum(i=1, n, 1/i^3))), ", "))

CROSSREFS

Cf. A055573.

Sequence in context: A331809 A126326 A284916 * A074793 A161767 A235333

Adjacent sequences:  A070983 A070984 A070985 * A070987 A070988 A070989

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 18 2002

STATUS

approved

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Last modified July 6 08:51 EDT 2020. Contains 335476 sequences. (Running on oeis4.)