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 A129658 Numerators of the convergents of the 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, 0, 1, 7, 8, 15, 23, 38, 61, 343, 404, 747, 7127, 29255, 387442, 1579023, 1966465, 5511953, 150789196, 156301149, 4527221368, 4683522517, 13894266402, 32472055321, 111310432365, 255092920051, 1896960872722, 2152053792773 (list; graph; refs; listen; history; text; internal format)
 OFFSET -2,5 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, ...], the convergents of which are 0/1, 1/0, [0/1], 1/1, 7/8, 8/9, 15/17, 23/26, 38/43, 61/69, 343/388, 404/457, 747/845, 7127/8062, 29255/33093, 387442/438271, 1579023/1786177, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence. MATHEMATICA nmax = 100; cfrac = ContinuedFraction[4 Pi^3/(81 Sqrt[3]), nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ] CROSSREFS Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129410, A129411. Cf. A129659, A129660, A129661, A129662, A129663, A129664, A129665. Sequence in context: A070424 A022097 A041100 * A041693 A042001 A020690 Adjacent sequences:  A129655 A129656 A129657 * A129659 A129660 A129661 KEYWORD nonn,frac,easy AUTHOR Stuart Clary, Apr 30 2007 STATUS approved

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Last modified March 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)