This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086241 #28 Feb 16 2025 08:32:50
%S A086241 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,
%T A086241 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,
%U A086241 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
%N 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.
%C A086241 It is not known if this series actually converges.
%D A086241 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, pp. 94-98.
%H A086241 Richard J. Mathar, <a href="https://arxiv.org/abs/1008.2547">Table of Dirichlet L-series...</a>, arXiv:1008.2547 [math.NT], 2010-2015, value of S(m=3,r=2,s=1).
%H A086241 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F A086241 Equals A161529 + A368644. - _Amiram Eldar_, Jan 02 2024
%e A086241 0.64194483853319570866139263972173431667541104401588965490817...
%t A086241 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 *)
%Y A086241 Cf. A161529, A368644.
%K A086241 nonn,cons,hard
%O A086241 0,1
%A A086241 _Eric W. Weisstein_, Jul 13 2003
%E A086241 More digits from _R. J. Mathar_, Jul 28 2010
%E A086241 Sign typo in definition corrected by _R. J. Mathar_, Aug 01 2010