A222227 Numbers n such that n and n + 16 are prime and there is a power of two in the interval (n,n+16).

3, 7, 13, 31, 241, 65521, 1048573, 2305843009213693951

Offset: 1

Author

Brad Clardy, Feb 23 2013

Keywords

• nonn

Comments

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

Crossrefs

Cf. A049488, A221211.

Programs

Magma

//Program finds primes separated by an even number (called gap) which
//have a power of two between them. Program starts with the smallest
//power of two above gap. Primes less than this starting point can be
//checked by inspection.
gap:=16;
start:=Ilog2(gap)+1;
for i:= start to 1000 do
    powerof2:=2^i;
    for k:=powerof2-gap+1 to powerof2-1 by 2 do
        if (IsPrime(k) and IsPrime(k+gap)) then k;
        end if;
    end for;
end for;