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 A093975 #14 Jun 11 2025 13:47:08
%S A093975 0,0,0,0,19,476,7180,86637,954456,9919519,99655858,979052296,
%T A093975 9484975460,91050561862,868774394325,8257228721817,78288453457352,
%U A093975 741199448968875
%N A093975 Number of prime pairs below 10^n having a difference of 42.
%H A093975 Siegfried "Zig" Herzog, <a href="http://zigherzog.net/primes/index.html#compare">Frequency of Occurrence of Prime Gaps</a>
%H A093975 T. Oliveira e Silva, S. Herzog, and S. Pardi, <a href="http://dx.doi.org/10.1090/S0025-5718-2013-02787-1">Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4.10^18</a>, Math. Comp., 83 (2014), 2033-2060.
%e A093975 a(6) = 476 because there are 476 prime gaps of 42 below 10^6.
%t A093975 Table[Count[Differences[Prime[Range[PrimePi[10^n]]]],42],{n,10}] (* The program generates the first 10 terms of the sequence. *) (* _Harvey P. Dale_, Jun 11 2025 *)
%Y A093975 Cf. A007508, A093974, A093976.
%K A093975 nonn,more
%O A093975 1,5
%A A093975 _Enoch Haga_, Apr 24 2004
%E A093975 a(10)-a(13) from _Washington Bomfim_, Jun 22 2012
%E A093975 a(14)-a(18) from S. Herzog's website added by _Giovanni Resta_, Aug 14 2018