%I #18 Sep 02 2024 01:28:47
%S 2,1,2,2,1,2,1,1,0,0,2,0,1,1,1,1,1,0,1,0,2,2,0,2,2,0,2,0,0,0,2,1,0,2,
%T 2,1,1,0,0,1,1,1,0,2,1,1,1,0,0,2,2,0,0,0,0,2,0,2,2,0,0,0,0,2,2,0,0,1,
%U 0,2,1,1,2,2,2,0,0,2,2,1,0,2,0,1,2,2,2,1,2,1,1,1,1,0,2,2,0,2,1,1
%N Expansion of L(3, chi3) in base 3, 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) = 0.8840238117500798567430579168710118077... = (0.2122121100201111101022022020002102211...)_3
%t nmax = 1000; First[ RealDigits[4 Pi^3/(81 Sqrt[3]) - (1/2) * 3^(-nmax), 3, nmax] ]
%Y Cf. A129404, A129405, 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