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Search: id:A153069
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| A153069 |
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Numerators of the convergents of the continued fraction for Catalan's constant L(2, chi4), where L(s, chi4) is the Dirichlet L-function for the non-principal character modulo 4. |
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7
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| 0, 1, 0, 1, 10, 11, 98, 109, 9690, 38869, 48559, 87428, 660555, 14619638, 15280193, 45180024, 150820265, 3966506914, 4117327179, 49257105883, 53374433062, 583001436503, 636375869565, 6310384262588, 19567528657329
(list; graph; listen)
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OFFSET
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-2,5
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FORMULA
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chi4(k) = Kronecker(-4, k); chi4(k) is 0, 1, 0, -1 when k reduced modulo 4 is 0, 1, 2, 3, respectively; chi4 is A101455.
Series: L(2, chi4) = sum_{k=1..infinity} chi4(k) k^{-2} = 1 - 1/3^2 + 1/5^2 - 1/7^2 + 1/9^2 - 1/11^2 + 1/13^2 - 1/15^2 + ...
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EXAMPLE
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L(2, chi4) = 0.91596559417721901505460351493238411... = [0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, ...], the convergents of which are 0/1, 1/0, [0/1], 1/1, 10/11,11/12,98/107,109/119,9690/10579,38869/42435,48559/53014,87428/95449,660555/721157, ..., 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[Catalan, nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]
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CROSSREFS
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Cf. A006752, A104338, A014538, A153070, A054543, A118323
Sequence in context: A046851 A045953 A136830 this_sequence A081551 A007088 A115848
Adjacent sequences: A153066 A153067 A153068 this_sequence A153070 A153071 A153072
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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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