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A153066 Continued fraction for L(2, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.

%I A153066 #6 Jan 31 2018 01:24:21
%S A153066 0,1,3,1,1,2,1,17,1,10,1,1,5,1,1,2,1,1,1,1,2,2,1,1,1,1,2,4,1,1,1,10,1,
%T A153066 2,1,1,1,6,1,12,2,14,1,1,1,3,3,1,1,3,1,1,12,3,1,1,1,2,1,1,6,3,1,1,4,2,
%U A153066 1,12,140,1,6,3,3,1,2,1100,4,1,1,2,1
%N A153066 Continued fraction for L(2, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
%F A153066 chi3(k) = Kronecker(-3, k); chi3(k) is 0, 1, -1 when k reduced modulo 3 is 0, 1, 2, respectively; chi3 is A102283.
%F A153066 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 + ...
%e A153066 L(2, chi3) = 0.781302412896486296867187429624092... = A086724 = = [0; 1, 3, 1, 1, 2, 1, 17, 1, 10, 1, 1, 5, 1, 1, 2, 1, ...]
%t A153066 nmax = 1000; ContinuedFraction[(Zeta[2, 1/3] - Zeta[2, 2/3])/9, nmax + 1]
%o A153066 (PARI) contfrac(zetahurwitz(2,1/3)/9 - zetahurwitz(2,2/3)/9) \\ _Charles R Greathouse IV_, Jan 31 2018
%Y A153066 Cf. A153067, A153068.
%K A153066 nonn,cofr,easy
%O A153066 0,3
%A A153066 _Stuart Clary_, Dec 17 2008