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 A093741 #20 Jun 24 2025 11:56:23
%S A093741 0,0,7,105,964,8005,65513,538382,4468957,37588207,319972455,
%T A093741 2753597777,23931289984,209796541197,1853552707266,16490531511496,
%U A093741 147632682729513,1329180643501191
%N A093741 Number of prime pairs below 10^n having a difference of 12.
%H A093741 Siegfried "Zig" Herzog, <a href="http://zigherzog.net/primes/index.html#compare">Frequency of Occurrence of Prime Gaps</a>
%H A093741 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 A093741 a(3) = 7 because there are 7 prime gaps of 12 below 10^3.
%t A093741 Table[Count[Differences[Prime[Range[PrimePi[10^n]]]],12],{n,10}] (* The program generates the first 10 terms of the sequence. *) (* _Harvey P. Dale_, Jun 24 2025 *)
%o A093741 (UBASIC) 20 N=1:dim T(34); 30 A=nxtprm(N); 40 N=A; 50 B=nxtprm(N); 60 D=B-A; 70 for x=2 to 34 step 2; 80 if D=X and B<10^2+1 then T(X)=T(X)+1; 90 next X; 100 if B>10^2+1 then 140; 110 B=A; 120 N=N+1; 130 goto 30; 140 for x=2 to 34 step 2; 150 print T(X);, 160 next (This program simultaneously finds values from 2 to 34 -- if gap=2 add 1-- adjust lines 80 and 100 for desired 10^n)
%Y A093741 Cf. A007508, A093740, A093742.
%K A093741 nonn,more
%O A093741 1,3
%A A093741 _Enoch Haga_, Apr 15 2004
%E A093741 a(10)-a(13) from _Washington Bomfim_, Jun 22 2012
%E A093741 a(14)-a(18) from S. Herzog's website added by _Giovanni Resta_, Aug 14 2018