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 A085994 #21 Aug 25 2021 15:28:24
%S A085994 0,0,4,1,8,1,5,4,3,4,4,9,7,0,2,4,5,9,6,1,4,3,0,6,3,3,4,3,5,2,8,1,4,6,
%T A085994 2,7,1,5,4,2,5,4,5,4,3,0,2,0,8,5,2,1,8,4,3,5,3,3,9,6,7,4,1,2,5,1,3,4,
%U A085994 5,5,7,4,1,5,9,9,5,0,9,1,9,5,0,5,6,7,2,7,4,9,3,5,2,6,8,9,5,7,6,9,2,2,8,3,8
%N A085994 Decimal expansion of the prime zeta modulo function at 5 for primes of the form 4k+3.
%H A085994 P. Flajolet and I. Vardi, <a href="http://algo.inria.fr/flajolet/Publications/landau.ps">Zeta Function Expansions of Classical Constants</a>, Unpublished manuscript. 1996.
%H A085994 X. Gourdon and P. Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.html">Some Constants from Number theory</a>.
%H A085994 R. J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli</a>, arXiv:1008.2547 [math.NT], 2010-2015, value P(m=4, n=3, s=5), page 21.
%H A085994 <a href="/index/Z#zeta_function">OEIS index to entries related to the (prime) zeta function</a>.
%F A085994 Zeta_R(5) = Sum_{primes r == 3 mod 4} 1/p^5
%F A085994 = (1/2)*Sum_{n=0..inf} mobius(2*n+1)*log(b((2*n+1)*5))/(2*n+1),
%F A085994 where b(x) = (1-2^(-x))*zeta(x)/L(x) and L(x) is the Dirichlet Beta function.
%e A085994 0.004181543449702459614306334352814627154254543020852184353396741251345574...
%t A085994 b[x_] = (1 - 2^(-x))*(Zeta[x]/DirichletBeta[x]); $MaxExtraPrecision = 200; m = 40; Join[{0, 0}, RealDigits[(1/2)*NSum[MoebiusMu[2n + 1]* Log[b[(2n + 1)*5]]/(2n + 1), {n, 0, m}, AccuracyGoal -> 120, NSumTerms -> m, PrecisionGoal -> 120, WorkingPrecision -> 120] ][[1]]][[1 ;; 105]] (* _Jean-François Alcover_, Jun 22 2011, updated Mar 14 2018 *)
%o A085994 (PARI) A085994_upto(N=100)={localprec(N+3); digits((PrimeZeta43(5)+1)\.1^N)[^1]} \\ see A085991 for the PrimeZeta43 function. - _M. F. Hasler_, Apr 25 2021
%Y A085994 Cf. A085991 .. A085998 (Zeta_R(2..9)).
%Y A085994 Cf. A086035 (analog for primes 4k+1), A085965 (PrimeZeta(5)), A002145 (primes 4k+3).
%K A085994 cons,nonn
%O A085994 0,3
%A A085994 Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003