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Search: id:A153068
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| A153068 |
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Denominators of the convergents of the continued fraction for L(2, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. |
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4
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| 1, 0, 1, 1, 4, 5, 9, 23, 32, 567, 599, 6557, 7156, 13713, 75721, 89434, 165155, 419744, 584899, 1004643, 1589542, 2594185, 6777912, 16150009, 22927921, 39077930, 62005851, 101083781, 264173413, 1157777433, 1421950846, 2579728279
(list; graph; listen)
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OFFSET
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-2,5
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FORMULA
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chi3(k) = Kronecker(-3, k); chi3(k) is 0, 1, -1 when k reduced modulo 3 is 0, 1, 2, respectively; chi3 is A102283.
Series: L(2, chi3) = sum_{k=1..infinity} chi3(k) k^{-2} = 1 - 1/2^2 + 1/4^2 - 1/5^2 + 1/7^2 - 1/8^2 + 1/10^2 - 1/11^2 + ...
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EXAMPLE
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L(2, chi3) = 0.781302412896486296867187429624092... = [0; 1, 3, 1, 1, 2, 1, 17, 1, 10, 1, 1, 5, 1, 1, 2, 1, ...], the convergents of which are 0/1, 1/0, [0/1], 1/1, 3/4, 4/5, 7/9, 18/23, 25/32, 443/567, 468/599, 5123/6557, 5591/7156, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence.
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MATHEMATICA
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nmax = 100; cfrac = ContinuedFraction[(Zeta[2, 1/3] - Zeta[2, 2/3])/9, nmax + 1]; Join[ {1, 0}, Denominator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]
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CROSSREFS
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Cf. A086724, A153066, A153067
Sequence in context: A153058 A041032 A041993 this_sequence A075116 A041079 A042715
Adjacent sequences: A153065 A153066 A153067 this_sequence A153069 A153070 A153071
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Dec 17, 2008
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