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%I #18 Dec 14 2017 03:42:18
%S 1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,0,0,0,1,
%T 0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0,1,1,0,1,1,0,1,
%U 1,1,0,0,1,0,0,0,0,1,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,1,1,1,0,1,1,1,1,1,1,0
%N Expansion of L(3, chi3) in base 2, where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
%C Contributed to OEIS on Apr 15 2007 -- the 300th anniversary of the birth of Leonhard Euler.
%D Leonhard Euler, "Introductio in Analysin Infinitorum", First Part, Articles 176 and 292
%F chi3(k) = Kronecker(-3, k); chi3(k) is 0, 1, -1 when k reduced modulo 3 is 0, 1, 2, respectively; chi3 is A049347 shifted.
%F Series: L(3, chi3) = sum_{k >= 1} chi3(k) k^{-3} = 1 - 1/2^3 + 1/4^3 - 1/5^3 + 1/7^3 - 1/8^3 + 1/10^3 - 1/11^3 + ...
%F Closed form: L(3, chi3) = 4 Pi^3/(81 sqrt(3)).
%e L(3, chi3) = A129404 = (0.111000100100111101100010011100000101101...)_2
%t nmax = 1000; First[ RealDigits[4 Pi^3/(81 Sqrt[3]) - (1/2) * 2^(-nmax), 2, nmax] ]
%Y Cf. A129404, A129406, A129407, A129408, A129409, A129410, A129411.
%Y Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
%K nonn,base,cons,easy
%O 0,1
%A _Stuart Clary_, Apr 15 2007
%E Offset corrected by _R. J. Mathar_, Feb 05 2009
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