A093739 - OEIS

%I #16 Aug 14 2018 09:05:58

%S 0,1,15,101,773,5569,42352,334180,2695109,22160841,185402143,

%T 1573331564,13515180171,117333792953,1028087693781,9081524454631,

%U 80799078096971,723494891844589

%N Number of prime pairs below 10^n having a difference of 8.

%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) = 15 because there are 15 prime gaps of 8 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, A093738, A093740.

%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