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 A387289 #12 Aug 25 2025 09:03:32
%S A387289 0,5,5,6,1,3,2,6,2,5,9,6,2,7,7,7,1,0,1,7,8,7,4,7,4,6,3,4,5,3,0,5,1,5,
%T A387289 2,9,0,1,8,0,3,7,2,6,6,1,0,0,2,8,8,4,3,8,7,4,6,5,0,4,0,1,0,3,6,2,5,6,
%U A387289 6,5,4,5,0,3,2,6,4,2,2,6,7,3,7,0,8,3,9,0,9,7,7,2,4,7,4,5,8,2,7,3,5,8,9,3,3,5
%N A387289 Decimal expansion of Sum_{n>=1} (-1)^(n+1) P(3*n)/(3*n), where P(x) is the prime zeta function.
%F A387289 Equals log(zeta(3)/zeta(6))/3.
%F A387289 Equals log(3*(35*zeta(3))^(1/3)/Pi^2).
%F A387289 Sum_{p prime} Sum_{n>=1} (-1)^(n+1)/p^(3*n)/(3*n) = Sum_{p prime} log((1+1/p^3))/3 = log(Product_{p prime} (1+1/p^3))/3 = log(zeta(3)/zeta(6))/3. - _Amiram Eldar_, Aug 25 2025
%e A387289 0.055613262596277710178747463453...
%t A387289 RealDigits[Log[Zeta[3]/Zeta[6]]/3, 10, 105, -1][[1]]
%Y A387289 Cf. A387293.
%K A387289 nonn,cons,new
%O A387289 0,2
%A A387289 _Artur Jasinski_, Aug 25 2025