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%I #7 Dec 10 2016 03:03:04
%S 1,8,13,16,64,6951,206515,344040,11364380,14595803,136951831,
%T 417525297,691111129,982473113,15154864245,17661539909,31435459113,
%U 49634203300,1454188399688,2112564552862,2266989878695,5056833185437,8740145960744
%N Pierce expansion of L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
%C Contributed to OEIS on April 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... = 1/1 - 1/(1*8) + 1/(1*8*13) - 1/(1*8*13*16) + 1/(1*8*13*16*64) - ...
%t nmax = 100; prec = 3000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Floor[ 1/(1 - #[[1]] #[[2]]) ], 1 - #[[1]] #[[2]]}&, {Floor[1/c], c}, nmax - 1]
%Y Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129411.
%Y Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665.
%K nonn,easy
%O 1,2
%A _Stuart Clary_, Apr 15 2007
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