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A153069 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. 6

%I

%S 0,1,0,1,10,11,98,109,9690,38869,48559,87428,660555,14619638,15280193,

%T 45180024,150820265,3966506914,4117327179,49257105883,53374433062,

%U 583001436503,636375869565,6310384262588,19567528657329

%N 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.

%F 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.

%F Series: L(2, chi4) = Sum_{k>=1} 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 + ...

%e 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.

%t nmax = 100; cfrac = ContinuedFraction[Catalan, nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]

%Y Cf. A006752, A014538, A054543, A104338, A118323, A153070.

%K nonn,frac,easy

%O -2,5

%A _Stuart Clary_, Dec 17 2008

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)