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A129406 Expansion of L(3, chi3) in base 3, where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. 15
2, 1, 2, 2, 1, 2, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 0, 2, 2, 0, 2, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Contributed to OEIS on Apr 15 2007 -- the 300th anniversary of the birth of Leonhard Euler.
REFERENCES
Leonhard Euler, "Introductio in Analysin Infinitorum", First Part, Articles 176 and 292
LINKS
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} 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)).
EXAMPLE
L(3, chi3) = 0.8840238117500798567430579168710118077... = (0.2122121100201111101022022020002102211...)_3
MATHEMATICA
nmax = 1000; First[ RealDigits[4 Pi^3/(81 Sqrt[3]) - (1/2) * 3^(-nmax), 3, nmax] ]
CROSSREFS
Sequence in context: A098199 A309474 A022828 * A123018 A336532 A100429
KEYWORD
nonn,base,cons,easy
AUTHOR
Stuart Clary, Apr 15 2007
EXTENSIONS
Offset corrected by R. J. Mathar, Feb 05 2009
STATUS
approved

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)