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 A343614 #8 Apr 26 2021 03:55:27
%S A343614 0,6,4,1,8,6,1,4,5,6,9,6,5,5,7,7,7,8,9,9,0,0,9,9,0,8,6,5,8,7,4,0,2,7,
%T A343614 3,6,8,0,9,7,5,6,3,6,2,3,4,8,6,8,0,6,4,0,8,8,4,6,2,5,4,9,2,2,5,0,6,2,
%U A343614 1,9,1,2,6,2,1,9,3,8,9,9,8,6,4,7,9,6,5,5,2,6,9,1,6,3,8,2,2,4,0,7
%N A343614 Decimal expansion of P_{3,2}(4) = Sum 1/p^4 over primes == 2 (mod 3).
%C A343614 The prime zeta modulo function P_{m,r}(s) = Sum_{primes p == r (mod m)} 1/p^s generalizes the prime zeta function P(s) = Sum_{primes p} 1/p^s.
%H A343614 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.
%H A343614 <a href="/index/Z#zeta_function">OEIS index to entries related to the (prime) zeta function</a>.
%F A343614 P_{3,2}(4) = P(4) - 1/3^4 - P_{3,1}(4) = A085964 - A021085 - A343624.
%e A343614 P_{3,2}(4) = 0.06418614569655777899009908658740273681...
%o A343614 (PARI) s=0;forprimestep(p=2,1e8,3,s+=1./p^4);s \\ For illustration: using primes up to 10^N gives about 3N+2 (= 26 for N=8) correct digits.
%o A343614 (PARI) A343614_upto(N=100)={localprec(N+5); digits((PrimeZeta32(4)+1)\.1^N)[^1]} \\ see for the function PrimeZeta32.
%Y A343614 Cf. A003627 (primes 3k-1), A085964 (PrimeZeta(4)), A021085 (1/3^4).
%Y A343614 Cf. A343624 (same for primes 3k+1), A086034 (for primes 4k+1), A085993 (for primes 4k+3), A343612 - A343619 (P_{3,2}(2..9): same for 1/p^2, ..., 1/p^9).
%K A343614 nonn,cons
%O A343614 0,2
%A A343614 _M. F. Hasler_, Apr 22 2021