|
%I #16 Aug 18 2018 06:56:50
%S 0,0,0,0,4,140,2403,33593,410754,4627165,49484726,511589763,
%T 5167085638,51359117940,504751212449,4920758221226,47694473239363,
%U 460356869024451
%N Number of prime pairs below 10^n having a difference of 54.
%C The primes must be consecutive, i.e., there must be no other primes between p and (p+54). - _Harvey P. Dale_, Aug 08 2011
%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(6) = 140 because there are 140 prime gaps of 54 below 10^6.
%t Table[Count[Partition[Prime[Range[PrimePi[10^i]]],2,1],_?(Last[#] - First[#] == 54&)],{i,9}] (* _Harvey P. Dale_, Aug 08 2011 *)
%Y Cf. A007508, A093980, A093982.
%K nonn,more
%O 1,5
%A _Enoch Haga_, Apr 24 2004
%E a(10)-a(13) from _Washington Bomfim_, Jun 22 2012
%E a(14)-a(18) from S. Herzog's website added by _Giovanni Resta_, Aug 14 2018
|
