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
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
KEYWORD
nonn,easy
AUTHOR
Stuart Clary, Apr 15 2007
STATUS
approved