The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A129661 Denominators of the Engel partial sums for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. 15
 1, 2, 4, 8, 112, 10528, 3916416, 453977888, 5984725643520, 24757413551258752, 36544913291284069002240, 3209228105587401803500707840, 206085396642453387914503205007360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Leonhard Euler, "Introductio in Analysin Infinitorum", First Part, Articles 176 and 292 LINKS FORMULA 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. 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 + ... Closed form: L(3, chi3) = 4 Pi^3/(81 sqrt(3)). EXAMPLE L(3, chi3) = 0.8840238117500798567430579168710118077... = 1/2 + 1/(2*2) + 1/(2*2*2) + 1/(2*2*2*14) + 1/(2*2*2*14*94) + ..., the partial sums of which are 0, 1/2, 3/4, 7/8, 99/112, 9307/10528, ... MATHEMATICA nmax = 100; prec = 2000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; e = First@Transpose@NestList[{Ceiling[1/(#[[1]] #[[2]] - 1)], #[[1]] #[[2]] - 1}&, {Ceiling[1/c], c}, nmax - 1]; Denominator[ FoldList[Plus, 0, 1/Drop[ FoldList[Times, 1, e], 1 ] ] ] CROSSREFS Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129410, A129411. Cf. A129658, A129659, A129660, A129662, A129663, A129664, A129665. Sequence in context: A018666 A018686 A018694 * A018713 A007633 A018777 Adjacent sequences:  A129658 A129659 A129660 * A129662 A129663 A129664 KEYWORD nonn,frac,easy AUTHOR Stuart Clary, Apr 30 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 14:38 EDT 2021. Contains 347618 sequences. (Running on oeis4.)