login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A153067 Numerators of the convergents of the 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, 0, 1, 3, 4, 7, 18, 25, 443, 468, 5123, 5591, 10714, 59161, 69875, 129036, 327947, 456983, 784930, 1241913, 2026843, 5295599, 12618041, 17913640, 30531681, 48445321, 78977002, 206399325, 904574302, 1110973627, 2015547929 (list; graph; refs; listen; history; text; internal format)
OFFSET

-2,5

LINKS

Table of n, a(n) for n=-2..29.

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... = [0; 1, 3, 1, 1, 2, 1, 17, 1, 10, 1, 1, 5, 1, 1, 2, 1, ...], the convergents of which are 0/1, 1/0, [0/1], 1/1, 3/4, 4/5, 7/9, 18/23, 25/32, 443/567, 468/599, 5123/6557, 5591/7156, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence.

MATHEMATICA

nmax = 100; cfrac = ContinuedFraction[(Zeta[2, 1/3] - Zeta[2, 2/3])/9, nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]

CROSSREFS

Cf. A086724, A153066, A153068.

Sequence in context: A327318 A093611 A042375 * A041593 A258740 A109749

Adjacent sequences:  A153064 A153065 A153066 * A153068 A153069 A153070

KEYWORD

nonn,frac,easy

AUTHOR

Stuart Clary, Dec 17 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 17 16:03 EDT 2021. Contains 343980 sequences. (Running on oeis4.)