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%I #18 Aug 14 2018 20:57:28
%S 0,0,16,119,916,7079,54431,430016,3484767,28764495,241298621,
%T 2052293026,17663498098,153590992984,1347587381486,11917605558274,
%U 106139298948562,951243890034661
%N Number of prime pairs below 10^n having a difference of 10.
%H Siegfried "Zig" Herzog, <a href="http://zigherzog.net/primes/index.html#compare">Frequency of Occurrence of Prime Gaps</a>
%H 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 a(3) = 16 because there are 16 prime gaps of 10 below 10^3.
%o (UBASIC)
%o 20 N=1:dim T(34);
%o 30 A=nxtprm(N);
%o 40 N=A;
%o 50 B=nxtprm(N);
%o 60 D=B-A;
%o 70 for x=2 to 34 step 2;
%o 80 if D=X and B<10^2+1 then T(X)=T(X)+1;
%o 90 next X;
%o 100 if B>10^2+1 then 140;
%o 110 B=A;
%o 120 N=N+1;
%o 130 goto 30;
%o 140 for x=2 to 34 step 2;
%o 150 print T(X);,
%o 160 next
%o ## (This program simultaneously finds values from 2 to 34 - if gap=2 add 1- adjust lines 80 and 100 for desired 10^n)
%Y Cf. A007508, A093739, A093741.
%K nonn,more
%O 1,3
%A _Enoch Haga_, Apr 15 2004
%E a(10)-a(13) from _Washington Bomfim_, Jun 20 2012
%E a(14)-a(18) from S. Herzog's website added by _Giovanni Resta_, Aug 14 2018
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