A222424 - OEIS

%I #17 Sep 08 2022 08:46:04

%S 3,5,23,29,53,59,509,1019,2039,262133,262139,536870909,

%T 73786976294838206459,2787593149816327892691964784081045188247543

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

%C It is a conjecture that this is a finite sequence. A search was conducted out to 2^1500.

%o (Magma)

%o //Program finds primes separated by an even number (called gap) which

%o //have a power of two between them. Program starts with the smallest

%o //power of two above gap. Primes less than this starting point can be

%o //checked by inspection.

%o gap:=14;

%o start:=Ilog2(gap)+1;

%o for i:= start to 1000 do

%o     powerof2:=2^i;

%o     for k:=powerof2-gap+1 to powerof2-1 by 2 do

%o         if (IsPrime(k) and IsPrime(k+gap)) then k;

%o         end if;

%o     end for;

%o end for;

%Y Cf. A153417, A221211.

%K nonn

%O 1,1

%A _Brad Clardy_, Feb 24 2013