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Search: id:A129407
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| A129407 |
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Balanced ternary 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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| 1, 0, -1, 0, 0, -1, -1, 1, 1, 0, 1, -1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, -1, 1, 0, -1, 1, -1, 0, 0, 1, -1, 1, 1, 0, -1, 1, 1, 0, 0, 1, 1, 1, 1, -1, 1, 1, 1, 0, 1, 0, -1, 0, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 1, 1, 0, -1, -1, 0, 0, -1, 0, 1, 0, -1, 1, 1, -1, 1, -1, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, 0, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1
(list; graph; listen)
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OFFSET
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0,1
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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 (for this constant); Articles 330 and 331 (for balanced ternary)
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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 + 0/3 - 1/3^2 + 0/3^3 + 0/3^4 - 1/3^5 - 1/3^6 + 1/3^7 + 1/3^8 + ...
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MATHEMATICA
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nmax = 1000; prec = nmax/2 + 20 (* Normally this is sufficient precision. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Round[3(#[[2]] - #[[1]])], 3(#[[2]] - #[[1]])}&, {Round[c], c}, nmax]
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CROSSREFS
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Cf. A129404, A129405, A129406, A129408, A129409, A129410, A129411.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A098033 A135022 A071982 this_sequence A014165 A014141 A014093
Adjacent sequences: A129404 A129405 A129406 this_sequence A129408 A129409 A129410
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KEYWORD
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sign,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007
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