A213210 Numbers n such that n and n + 8 are prime and there is a power of two in the interval (n,n+8).

3, 5, 11, 29, 59, 4091, 262139

Offset: 1

Author

Brad Clardy, Mar 02 2013

Keywords

• nonn

Comments

It is a conjecture that this sequence is finite. A search around 2^n was done up to 2^1500.

Crossrefs

Cf. A023202, A221211.

Programs

Magma

//Program finds primes separated by an even number (called gap) which
//have a power of two between them. The program starts with the smallest
//power of two above gap. Primes less than this starting point can be
//checked inspection. In this example 3 and 5 also work.
gap:=8;
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;

Magma

[n: n in PrimesUpTo(10^6) | IsPrime(n+8) and exists{t: t in [n+1..n+7 by 2] | IsOne(t/2^Valuation(t,2))}]; // Bruno Berselli, May 16 2013