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 A307385 #9 Jul 09 2019 13:07:04
%S A307385 0,4,5,2,9,4,3,4,8,8,5,0
%N A307385 Decimal expansion of the constant S_2* = Sum_{j>=1} prime((2*j + 1) - 1)!/prime((2*j + 2) - 1)!.
%C A307385 The constant S_2* is related to the prime gaps, since twin primes produce the largest terms of the sum compared with neighboring terms.
%C A307385 On Apr 06 2019, the first 4200000000 prime numbers were used in order to calculate S_1* and S_2* and using Rosser's theorem we get: 0.04529434885014 < S_1* + S_2* < 0.04529434885035.
%H A307385 Wikipedia, <a href="https://en.wikipedia.org/wiki/Rosser%27s_theorem">Rosser's theorem</a>
%F A307385 S_2* = Sum_{j>=1} prime((2*j + 1) - 1)!/prime((2*j + 2) - 1)! = Sum_{j>=1} 1/(Product{k=prime(2*j + 1), prime((2*j + 2) - 1)} k) = 1/(5*6) + 1/(11*12) + 1/(17*18) + 1/(23*24*25*26*27*28) +...
%e A307385 S_2* = 0.045294348850...
%Y A307385 Cf. A000040, A306658 (S_1) A306700 (S_2), A306744 (S_1 + S_2), A307383 (S_1* + S_2*), A307384 (S_1*).
%K A307385 cons,nonn,more
%O A307385 0,2
%A A307385 _Marco Ripà_ and _Aldo Roberto Pessolano_, Apr 06 2019