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 A331369 #29 May 13 2020 02:56:23
%S A331369 0,2,9,9,8,1,7,1,0,8,3,8,9,0,6,2,6,9,6,8,2,6
%N A331369 Decimal expansion of Sum_{(p1, p2) is twin prime pair} 1/p1 + 1/p2 - log(p2/p1).
%C A331369 Let (p_k, p_(k+1)) twin prime pair. Then log(p_(k+1)/p_k) < 1/p_k + 1/p_(k+1).
%C A331369 Lim_{k -> oo} 1/p_k + 1/p_(k+1) - log(p_(k+1)/p_k) = 0.
%C A331369 This constant is analogous to Euler-Mascheroni constant for twin primes.
%F A331369 Equals Sum_{k >= 1} 1/A001359(k) + 1/A006512(k) - log(A006512(k)/A001359(k)).
%e A331369 0.0299817108389062696826...
%o A331369 (PARI) p = 3; st = 0.0; forprime(n = 5, 1e11, if(n - p == 2, st += 1/p + 1/n - log(n/p)); p = n); print(st)
%Y A331369 Cf. A077800, A065421, A001359, A006512, A077761.
%K A331369 nonn,cons,more
%O A331369 0,2
%A A331369 _Dimitris Valianatos_, May 03 2020