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 A129408 Continued fraction for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. 15
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Contributed to OEIS on April 15, 2007 -- the 300th anniversary of the birth of Leonhard Euler. 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} 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... = [0; 1, 7, 1, 1, 1, 1, 1, 5, 1, 1, 9, 4, 13, 4, ...]. MATHEMATICA nmax = 1000; ContinuedFraction[4 Pi^3/(81 Sqrt[3]), nmax + 1] CROSSREFS Cf. A129404, A129405, A129406, A129407, A129409, A129410, A129411. Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665. Sequence in context: A117825 A010143 A101027 * A339748 A325470 A240831 Adjacent sequences:  A129405 A129406 A129407 * A129409 A129410 A129411 KEYWORD nonn,cofr,easy AUTHOR Stuart Clary, Apr 15 2007 STATUS approved

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Last modified August 4 09:33 EDT 2021. Contains 346446 sequences. (Running on oeis4.)