%I A129664
%S A129664 0,1,5,53,25619,73767966817,388826530522004941794623,
%T A129664 226073434564505101198889656344981223287273794070917,
%U A129664 302470760179203901700754265690364240921018701177125350099844323581396873793766696160680079412655525143887
%N A129664 Numerators of the greedy Egyptian partial sums for L(3, chi3), where 
               L(s, chi3) is the Dirichlet L-function for the non-principal character 
               modulo 3.
%D A129664 Leonhard Euler, ``Introductio in Analysin Infinitorum'', First Part, 
               Articles 176 and 292
%F A129664 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 A129664 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 A129664 Closed form: L(3, chi3) = 4 pi^3/(81 sqrt(3))
%e A129664 L(3, chi3) = 0.8840238117500798567430579168710118077... = 1/2 + 1/3 + 
               1/20 + 1/1449 + 1/2879423 + ..., the partial sums of which are 0, 
               1/2, 5/6, 53/60, 25619/28980, 73767966817/83445678540, ...
%t A129664 nmax = 12; prec = 2000 (* Adjust the precision depending on nmax. *); 
               c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; e = First@Transpose@NestList[{Ceiling[1/
               (#[[2]] - 1/#[[1]])], #[[2]] - 1/#[[1]]}&, {Ceiling[1/c], c}, nmax 
               - 1]; Numerator[ FoldList[Plus, 0, 1/e] ]
%Y A129664 Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129410, A129411.
%Y A129664 Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129665.
%Y A129664 Sequence in context: A048551 A083757 A093674 this_sequence A087125 A110430 
               A110432
%Y A129664 Adjacent sequences: A129661 A129662 A129663 this_sequence A129665 A129666 
               A129667
%K A129664 nonn,frac,easy
%O A129664 0,3
%A A129664 Stuart Clary (clary(AT)uakron.edu), Apr 30, 2007