OFFSET
0,1
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
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) = A129404 = (0.111000100100111101100010011100000101101...)_2
MATHEMATICA
nmax = 1000; First[ RealDigits[4 Pi^3/(81 Sqrt[3]) - (1/2) * 2^(-nmax), 2, nmax] ]
CROSSREFS
KEYWORD
AUTHOR
Stuart Clary, Apr 15 2007
EXTENSIONS
Offset corrected by R. J. Mathar, Feb 05 2009
STATUS
approved