A220746 Numbers n such that n and n + 10 are prime and there is a power of two in the interval (n, n+10).

3, 7, 13, 31, 61, 127, 1021, 1048573, 23945242826029513411849172299223580994042798784118781

Offset: 1

Author

Brad Clardy, Feb 20 2013

Keywords

• nonn

Crossrefs

Cf. A023203, 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. In this example 3 also works.
gap:=10;
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;

Mathematica

Union[Flatten[Table[Select[Range[2^n - 9, 2^n - 1, 2], PrimeQ[#] && PrimeQ[# + 10] &], {n, 3, 200}]]] (* T. D. Noe, Feb 20 2013 *)
Union[Flatten[Table[Select[Thread[{Range[2^n-10,2^n],Range[ 2^n,2^n+10]}],AllTrue[ #,PrimeQ]&],{n,3,1000}],1][[;;,1]]] (* Harvey P. Dale, Feb 19 2023 *)

PARI

print1(3); for(n=4,500,forprime(p=2^n-9,2^n-1,if(isprime(p+10), print1(", "p)))) \\ Charles R Greathouse IV, Feb 20 2013