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 A286229 #11 Feb 16 2025 08:33:44
%S A286229 1,9,4,1,1,8,1,6,9,8,3,2,6,3,3,7,9,2,2,9,9,5,8,7,4,8,4,9,1,1,3,8,0,8,
%T A286229 3,7,4,5,1,8,7,7,0,1,8,4,5,2,7,9,2,1,9,7,7,3,5,0,4,3,4,9,4,0,4,1,0,3,
%U A286229 8,0,8,7,4,2,0,5,7,9,2,5,2,6,3,3,9,3,9,5,3,9,8,7,7,6,5,4,3,5,3,6,7,8,8,2,3
%N A286229 Decimal expansion of Sum_{p prime} 1/(p^3 - 1).
%H A286229 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>.
%H A286229 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F A286229 Equals Sum_{k>=1} primezeta(3*k).
%F A286229 More generally, Sum_{p prime} 1/(p^s - 1) = Sum_{k>=1} primezeta(s*k).
%e A286229 1/(2^3 - 1) + 1/(3^3 - 1) + 1/(5^3 - 1) + ... = 1/2^3 + 1/3^3 + 1/5^3 + ... + 1/2^6 + 1/3^6 + 1/5^6 + ... + 1/2^9 + 1/3^9 + 1/5^9 + ... = 0.19411816983263379229...
%t A286229 digits = 105; sp = NSum[PrimeZetaP[3 n], {n, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 2*digits]; RealDigits[sp, 10, digits] // First
%o A286229 (PARI) sumeulerrat(1/(p^3-1)) \\ _Amiram Eldar_, Mar 18 2021
%Y A286229 Cf. A030078, A085541, A154945.
%K A286229 nonn,cons
%O A286229 0,2
%A A286229 _Ilya Gutkovskiy_, May 04 2017