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Search: id:A070987
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| A070987 |
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Number of terms in simple continued fraction for sum(k=1,n,1/k^4). |
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+0
1
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| 1, 2, 8, 8, 9, 12, 22, 23, 27, 29, 33, 33, 49, 39, 48, 52, 58, 62, 65, 68, 73, 67, 75, 72, 80, 83, 87, 89, 100, 91, 93, 109, 113, 112, 101, 105, 107, 118, 123, 131, 118, 120, 123, 141, 151, 148, 157, 165, 157, 170, 180, 158, 187, 181, 181, 195, 187, 181, 194, 188
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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sum(k>=1,1/k^4)=zeta(4)=Pi^4/90
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FORMULA
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lim n ->infinity a(n)/n=C=3, 3....
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EXAMPLE
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The simple continued fraction for sum(k=1,10,1/k^4) is [1, 12, 5, 3, 1, 2, 10, 12, 1, 2, 4, 2, 2, 2, 1, 7, 11, 1, 1, 2, 5, 2, 2, 4, 3, 1, 1, 1, 2] which contains 29 terms, hence a(10)=29.
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PROGRAM
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(PARI) for(n=1, 100, print1(length(contfrac(sum(i=1, n, 1/i^4))), ", "))
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CROSSREFS
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Cf. A055573.
Adjacent sequences: A070984 A070985 A070986 this_sequence A070988 A070989 A070990
Sequence in context: A137575 A143812 A092280 this_sequence A079458 A138230 A128018
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 18 2002
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