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Search: id:A129411
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| A129411 |
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Greedy Egyptian 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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16
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| 2, 3, 20, 1449, 2879423, 31625640285294, 1162849840832612010600369938, 4013794377413687199924671384130798842309412001723286013, 32025095658857878502181254937184611855940944199483548417530154807379258429933254\ 996925647878294253643673560013
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Contributed to OEIS on Apr 15, 2007 --- the 300th anniversary of the birth of Leonhard Euler.
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REFERENCES
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Leonhard Euler, ``Introductio in Analysin Infinitorum'', First Part, Articles 176 and 292
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FORMULA
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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
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L(3, chi3) = 0.8840238117500798567430579168710118077... = 1/2 + 1/3 + 1/20 + 1/1449 + 1/2879423 + ...
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MATHEMATICA
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nmax = 12; prec = 2000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Ceiling[1/(#[[2]] - 1/#[[1]])], #[[2]] - 1/#[[1]]}&, {Ceiling[1/c], c}, nmax - 1]
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CROSSREFS
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Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129410.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A110372 A132421 A132500 this_sequence A124447 A024765 A090122
Adjacent sequences: A129408 A129409 A129410 this_sequence A129412 A129413 A129414
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KEYWORD
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nonn,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007
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