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A129405
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Expansion of L(3, chi3) in base 2, 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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1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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... = (0.111000100100111101100010011100000101101...)_2
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MATHEMATICA
| nmax = 1000; First[ RealDigits[4 Pi^3/(81 Sqrt[3]) - (1/2) * 2^(-nmax), 2, nmax] ]
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CROSSREFS
| Cf. A129404, A129406, A129407, A129408, A129409, A129410, A129411.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A016362 A016415 A127693 * A127001 A068431 A143466
Adjacent sequences: A129402 A129403 A129404 * A129406 A129407 A129408
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KEYWORD
| nonn,cons,easy
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AUTHOR
| Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007
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EXTENSIONS
| Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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