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A129410 Pierce expansion of L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. 15
1, 8, 13, 16, 64, 6951, 206515, 344040, 11364380, 14595803, 136951831, 417525297, 691111129, 982473113, 15154864245, 17661539909, 31435459113, 49634203300, 1454188399688, 2112564552862, 2266989878695, 5056833185437, 8740145960744 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Contributed to OEIS on April 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=1..23.

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... = 1/1 - 1/(1*8) + 1/(1*8*13) - 1/(1*8*13*16) + 1/(1*8*13*16*64) - ...

MATHEMATICA

nmax = 100; prec = 3000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Floor[ 1/(1 - #[[1]] #[[2]]) ], 1 - #[[1]] #[[2]]}&, {Floor[1/c], c}, nmax - 1]

CROSSREFS

Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129411.

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

Sequence in context: A272486 A057486 A188198 * A338598 A168339 A070112

Adjacent sequences:  A129407 A129408 A129409 * A129411 A129412 A129413

KEYWORD

nonn,easy

AUTHOR

Stuart Clary, Apr 15 2007

STATUS

approved

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)