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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. 3
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

S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 94-98.

LINKS

Table of n, a(n) for n=0..97.

R. J. Mathar, Table of Dirichlet L-series..., arXiv:1008.2547 [math.NT], 2010-2015, value of S(m=3,r=2,s=1).

Eric Weisstein's World of Mathematics, Prime Sums

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

Sequence in context: A309222 A324034 A343614 * A204023 A166905 A278071

Adjacent sequences:  A086238 A086239 A086240 * A086242 A086243 A086244

KEYWORD

nonn,cons,hard

AUTHOR

Eric W. Weisstein, Jul 13 2003

EXTENSIONS

More digits from R. J. Mathar, Jul 28 2010

Sign typo in definition corrected by R. J. Mathar, Aug 01 2010

STATUS

approved

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Last modified October 1 09:13 EDT 2022. Contains 357140 sequences. (Running on oeis4.)