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.

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

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

Table of n, a(n) for n=0..99.

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

Cf. A129404, A129405, A129407, A129408, A129409, A129410, A129411.

Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665.

Sequence in context: A309474 A378256 A022828 * A123018 A336532 A100429

Adjacent sequences: A129403 A129404 A129405 * A129407 A129408 A129409

Keyword

nonn,base,cons,easy

Author

Stuart Clary, Apr 15 2007

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009

Status

approved