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A129409
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Engel expansion of L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
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15
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2, 2, 2, 14, 94, 372, 1391, 7690, 17729, 49204, 87816, 128433, 151275, 290477, 297212, 299837, 352249, 897751, 1081032, 1646358, 2402614, 36591866, 49132456, 93538655, 141789387, 180474393, 687775235, 851204316, 1868593596, 7042652755
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Contributed to OEIS on Apr 15, 2007 --- the 300th anniversary of the birth of Leonhard Euler.
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REFERENCES
| Leonhard Euler, ``Introductio in Analysin Infinitorum'', First Part, Articles 176 and 292
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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))
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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) + ...
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MATHEMATICA
| nmax = 100; prec = 2000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Ceiling[1/(#[[1]] #[[2]] - 1)], #[[1]] #[[2]] - 1}&, {Ceiling[1/c], c}, nmax - 1]
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CROSSREFS
| Cf. A129404, A129405, A129406, A129407, A129408, A129410, A129411.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A183584 A063898 A074052 * A025521 A068218 A098919
Adjacent sequences: A129406 A129407 A129408 * A129410 A129411 A129412
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KEYWORD
| nonn,easy
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AUTHOR
| Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007
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