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 A271951 #11 Feb 16 2025 08:33:33
%S A271951 1,1,5,0,4,8,0,7,7,2,3,5,6,6,1,8,5,2,7,2,7,8,4,8,8,0,7,4,3,7,4,6,9,8,
%T A271951 0,9,0,6,3,0,3,9,3,2,9,8,5,1,1,0,8,3,6,8,0,6,8,8,1,9,3,0,5,9,0,2,2,8,
%U A271951 2,6,3,2,3,2,5,4,3,8,0,1,3,7,1,5,7,4,0,5,2,0,9,2,9,9,4,3,6,3,8
%N A271951 Decimal expansion of (1/2) Product_{p prime} 1+1/(p-1)^3, a constant related to I. M. Vinogradov's proof of the "ternary" Goldbach conjecture.
%D A271951 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 88.
%H A271951 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/GoldbachConjecture.html">Goldbach Conjecture</a>.
%H A271951 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/VinogradovsTheorem.html">Vinogradov's theorem</a>.
%H A271951 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>.
%H A271951 Wikipedia, <a href="https://en.wikipedia.org/wiki/Vinogradov's_theorem">Vinogradov's theorem</a>.
%e A271951 1.150480772356618527278488074374698090630393298511083680688193059...
%t A271951 $MaxExtraPrecision = 1600; digits = 99; terms = 1600; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0, 0}, LinearRecurrence[{4, -6, 3}, {3, 12, 30}, terms + 10]]; r[n_Integer] := LR[[n]]; (1/2) Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First
%o A271951 (PARI) (1/2) * prodeulerrat(1+1/(p-1)^3) \\ _Amiram Eldar_, Mar 14 2021
%Y A271951 Cf. A005597.
%K A271951 nonn,cons
%O A271951 1,3
%A A271951 _Jean-François Alcover_, Apr 17 2016