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A153066 Continued fraction for L(2, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. 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 (list; graph; refs; listen; history; text; internal format)
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: A095276 A246457 A089338 * A126209 A176346 A073166

Adjacent sequences:  A153063 A153064 A153065 * A153067 A153068 A153069

KEYWORD

nonn,cofr,easy

AUTHOR

Stuart Clary, Dec 17 2008

STATUS

approved

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Last modified February 22 17:14 EST 2020. Contains 332140 sequences. (Running on oeis4.)