A153066 Continued fraction for L(2, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.

0, 1, 3, 1, 1, 2, 1, 17, 1, 10, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 4, 1, 1, 1, 10, 1, 2, 1, 1, 1, 6, 1, 12, 2, 14, 1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 12, 3, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 4, 2, 1, 12, 140, 1, 6, 3, 3, 1, 2, 1100, 4, 1, 1, 2, 1

Offset

0,3

Links

Table of n, a(n) for n=0..80.

Formula

chi3(k) = Kronecker(-3, k); chi3(k) is 0, 1, -1 when k reduced modulo 3 is 0, 1, 2, respectively; chi3 is A102283.

Series: L(2, chi3) = sum_{k=1..infinity} chi3(k) k^{-2} = 1 - 1/2^2 + 1/4^2 - 1/5^2 + 1/7^2 - 1/8^2 + 1/10^2 - 1/11^2 + ...

Example

L(2, chi3) = 0.781302412896486296867187429624092... = A086724 = = [0; 1, 3, 1, 1, 2, 1, 17, 1, 10, 1, 1, 5, 1, 1, 2, 1, ...]

Mathematica

nmax = 1000; ContinuedFraction[(Zeta[2, 1/3] - Zeta[2, 2/3])/9, nmax + 1]

Prog

(PARI) contfrac(zetahurwitz(2, 1/3)/9 - zetahurwitz(2, 2/3)/9) \\ Charles R Greathouse IV, Jan 31 2018

Crossrefs

Cf. A153067, A153068.

Sequence in context: A246457 A089338 A356400 * A126209 A176346 A338878

Adjacent sequences: A153063 A153064 A153065 * A153067 A153068 A153069

Keyword

nonn,cofr,easy

Author

Stuart Clary, Dec 17 2008

Status

approved