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Search: id:A129664
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| A129664 |
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Numerators of the greedy Egyptian partial sums for 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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| 0, 1, 5, 53, 25619, 73767966817, 388826530522004941794623, 226073434564505101198889656344981223287273794070917, 30247076017920390170075426569036424092101870117712535009984432358139687379376669\ 6160680079412655525143887
(list; graph; listen)
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OFFSET
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0,3
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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 + ..., the partial sums of which are 0, 1/2, 5/6, 53/60, 25619/28980, 73767966817/83445678540, ...
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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]; e = First@Transpose@NestList[{Ceiling[1/(#[[2]] - 1/#[[1]])], #[[2]] - 1/#[[1]]}&, {Ceiling[1/c], c}, nmax - 1]; Numerator[ FoldList[Plus, 0, 1/e] ]
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CROSSREFS
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Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129410, A129411.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129665.
Sequence in context: A048551 A083757 A093674 this_sequence A087125 A110430 A110432
Adjacent sequences: A129661 A129662 A129663 this_sequence A129665 A129666 A129667
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Apr 30, 2007
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