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 A242301 #47 Feb 16 2025 08:33:22
%S A242301 1,6,2,8,1,6,2,4,6,6,6,3,6,0,1,4
%N A242301 Decimal expansion of C(2), where C(x) = -Sum{k>=1} (-1)^k/prime(k)^x.
%C A242301 The alternating series of reciprocal powers of prime numbers converges for any x > 0 (absolutely so if x > 1) but is hard to compute.
%C A242301 The next digits of C(2), after ...6014, seem to converge to a(16)=1, a(17)=5.
%H A242301 Stanislav Sykora, <a href="https://oeis.org/wiki/File:PrimesRelatedFunctions.txt">PARI/GP scripts for primes-related functions</a>, see function AltSum1DivPrimePwr(x,eps), with instructions.
%H A242301 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>
%H A242301 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>
%H A242301 Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_zeta_function">Prime Zeta Function</a>
%e A242301 0.1628162466636014...
%t A242301 k = 1; p = 2; s = 0; While[p < 1000000000, s = N[s + (-1)^k/p^2, 40]; k = Mod[++k, 2]; p = NextPrime@ p]; s (* takes ~30 minutes on an average laptop to 18 decimal digits *)(* _Robert G. Wilson v_, Dec 30 2017 *)
%o A242301 (PARI) See Sykora link.
%Y A242301 Cf. A078437 (x=1), A242302 (x=3), A242303 (x=4), A242304 (x=5).
%Y A242301 Cf. A085548.
%K A242301 nonn,cons,hard,more
%O A242301 0,2
%A A242301 _Stanislav Sykora_, May 14 2014