%I A129408
%S A129408 0,1,7,1,1,1,1,1,5,1,1,9,4,13,4,1,2,27,1,28,1,2,2,3,2,7,1,1,19,1,8,3,3,
%T A129408 2,1,10,1,1,1,1,1,1,2,3,1,1,35,1,2,91,1,1,1,4,1,1,1,1,1,2,16,1,2,2,1,2,
%U A129408 6,1,1,6,14,1,5,5,14,2,8,1,1,1,1,2,4,2,10,37,1,10,2,4,5,4,5,24,1,2,7,1
%N A129408 Continued fraction for L(3, chi3), where L(s, chi3) is the Dirichlet 
               L-function for the non-principal character modulo 3.
%C A129408 Contributed to OEIS on April 15, 2007 --- the 300th anniversary of the 
               birth of Leonhard Euler.
%D A129408 Leonhard Euler, ``Introductio in Analysin Infinitorum'', First Part, 
               Articles 176 and 292
%F A129408 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 A129408 Series: L(3, chi3) = sum_{k=1..infinity} 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 A129408 Closed form: L(3, chi3) = 4 pi^3/(81 sqrt(3))
%e A129408 L(3, chi3) = 0.8840238117500798567430579168710118077... = [0; 1, 7, 1, 
               1, 1, 1, 1, 5, 1, 1, 9, 4, 13, 4, ...]
%t A129408 nmax = 1000; ContinuedFraction[4 Pi^3/(81 Sqrt[3]), nmax + 1]
%Y A129408 Cf. A129404, A129405, A129406, A129407, A129409, A129410, A129411.
%Y A129408 Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
%Y A129408 Sequence in context: A117825 A010143 A101027 this_sequence A140213 A091258 
               A072101
%Y A129408 Adjacent sequences: A129405 A129406 A129407 this_sequence A129409 A129410 
               A129411
%K A129408 nonn,cofr,easy
%O A129408 0,3
%A A129408 Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007