cp's OEIS Frontend

A222424 Numbers n such that n and n + 14 are prime and there is a power of two in the interval (n,n+14).

%I A222424 #17 Sep 08 2022 08:46:04
%S A222424 3,5,23,29,53,59,509,1019,2039,262133,262139,536870909,
%T A222424 73786976294838206459,2787593149816327892691964784081045188247543
%N A222424 Numbers n such that n and n + 14 are prime and there is a power of two in the interval (n,n+14).
%C A222424 It is a conjecture that this is a finite sequence. A search was conducted out to 2^1500.
%o A222424 (Magma)
%o A222424 //Program finds primes separated by an even number (called gap) which
%o A222424 //have a power of two between them. Program starts with the smallest
%o A222424 //power of two above gap. Primes less than this starting point can be
%o A222424 //checked by inspection.
%o A222424 gap:=14;
%o A222424 start:=Ilog2(gap)+1;
%o A222424 for i:= start to 1000 do
%o A222424     powerof2:=2^i;
%o A222424     for k:=powerof2-gap+1 to powerof2-1 by 2 do
%o A222424         if (IsPrime(k) and IsPrime(k+gap)) then k;
%o A222424         end if;
%o A222424     end for;
%o A222424 end for;
%Y A222424 Cf. A153417, A221211.
%K A222424 nonn
%O A222424 1,1
%A A222424 _Brad Clardy_, Feb 24 2013