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 A129659 Denominators 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
 1, 0, 1, 1, 8, 9, 17, 26, 43, 69, 388, 457, 845, 8062, 33093, 438271, 1786177, 2224448, 6235073, 170571419, 176806492, 5121153195, 5297959687, 15717072569, 36732104825, 125913387044, 288558878913, 2145825539435, 2434384418348 (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..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... = [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[ {1, 0}, Denominator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ] CROSSREFS Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129410, A129411. Cf. A129658, A129660, A129661, A129662, A129663, A129664, A129665. Sequence in context: A274406 A261454 A022098 * A041130 A041307 A042289 Adjacent sequences:  A129656 A129657 A129658 * A129660 A129661 A129662 KEYWORD nonn,frac,easy AUTHOR Stuart Clary, Apr 30 2007 STATUS approved

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Last modified May 13 08:08 EDT 2021. Contains 343836 sequences. (Running on oeis4.)