|
|
A086241
|
|
Decimal expansion of value to which Sum_{k>=2} d(k)/prime(k) appears to converge, where d(k)=-1 if p mod 3 = 1, d(k)=+1 if p mod 3 = 2 and d(k)=0 if p mod 3 = 0.
|
|
5
|
|
|
6, 4, 1, 9, 4, 4, 8, 3, 8, 5, 3, 3, 1, 9, 5, 7, 0, 8, 6, 6, 1, 3, 9, 2, 6, 3, 9, 7, 2, 1, 7, 3, 4, 3, 1, 6, 6, 7, 5, 4, 1, 1, 0, 4, 4, 0, 1, 5, 8, 8, 9, 6, 5, 4, 9, 0, 8, 1, 7, 0, 8, 4, 5, 1, 3, 1, 7, 3, 3, 2, 8, 2, 6, 9, 0, 7, 3, 7, 2, 3, 3, 5, 9, 8, 1, 7, 4, 1, 5, 9, 9, 4, 5, 6, 0, 6, 5, 7
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
It is not known if this series actually converges.
|
|
REFERENCES
|
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, pp. 94-98.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Prime Sums.
|
|
FORMULA
|
|
|
EXAMPLE
|
0.64194483853319570866139263972173431667541104401588965490817...
|
|
MATHEMATICA
|
S[m_, n_, s_] := (t = 1; sums = 0; difs = 1; While[Abs[difs] > 10^(-digits - 5) || difs == 0, difs = (MoebiusMu[t]/t) * Log[If[s*t == 1, DirichletL[m, n, s*t], Sum[Zeta[s*t, j/m]*DirichletCharacter[m, n, j]^t, {j, 1, m}]/m^(s*t)]]; sums = sums + difs; t++]; sums); $MaxExtraPrecision = 1000; digits = 121; RealDigits[Chop[N[-S[3, 2, 1], digits]], 10, digits-1][[1]] (* Vaclav Kotesovec, Jan 22 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Sign typo in definition corrected by R. J. Mathar, Aug 01 2010
|
|
STATUS
|
approved
|
|
|
|