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A129409 Engel expansion of L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. 15
2, 2, 2, 14, 94, 372, 1391, 7690, 17729, 49204, 87816, 128433, 151275, 290477, 297212, 299837, 352249, 897751, 1081032, 1646358, 2402614, 36591866, 49132456, 93538655, 141789387, 180474393, 687775235, 851204316, 1868593596, 7042652755 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
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... = 1/2 + 1/(2*2) + 1/(2*2*2) + 1/(2*2*2*14) + 1/(2*2*2*14*94) + ...
MATHEMATICA
nmax = 100; prec = 2000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Ceiling[1/(#[[1]] #[[2]] - 1)], #[[1]] #[[2]] - 1}&, {Ceiling[1/c], c}, nmax - 1]
CROSSREFS
Sequence in context: A350599 A361815 A349564 * A352029 A025521 A305109
KEYWORD
nonn,easy
AUTHOR
Stuart Clary, Apr 15 2007
STATUS
approved

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)