A093739 Number of prime pairs below 10^n having a difference of 8.

0, 1, 15, 101, 773, 5569, 42352, 334180, 2695109, 22160841, 185402143, 1573331564, 13515180171, 117333792953, 1028087693781, 9081524454631, 80799078096971, 723494891844589

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Siegfried "Zig" Herzog, Frequency of Occurrence of Prime Gaps

T. Oliveira e Silva, S. Herzog, and S. Pardi, Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4.10^18, Math. Comp., 83 (2014), 2033-2060.

Example

a(3) = 15 because there are 15 prime gaps of 8 below 10^3.

Prog

(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)

Crossrefs

Cf. A007508, A093738, A093740.

Sequence in context: A242657 A163717 A111370 * A205431 A085465 A205424

Adjacent sequences: A093736 A093737 A093738 * A093740 A093741 A093742

Keyword

nonn,more

Author

Enoch Haga, Apr 15 2004

Extensions

a(10)-a(13) from Washington Bomfim, Jun 20 2012

a(14)-a(18) from S. Herzog's website added by Giovanni Resta, Aug 14 2018

Status

approved