A222219 Numbers n such that n and n + 18 are prime and there is a power of two in the interval (n,n+18).

5, 11, 13, 19, 23, 29, 53, 61, 113, 239, 251, 503, 1013, 1021, 4093, 8191, 65519, 65521, 262133, 1048571, 4194301, 302231454903657293676533

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..22.

Mathematica

Flatten[Table[Select[2^n-Range[17], AllTrue[{#, #+18}, PrimeQ]&], {n, 4, 80}]]// Sort (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 04 2019 *)

Prog

(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:=18;
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;

Crossrefs

Cf. A153418, A221211.

Sequence in context: A079019 A191034 A340466 * A023225 A206581 A292940

Adjacent sequences: A222216 A222217 A222218 * A222220 A222221 A222222

Keyword

nonn

Author

Brad Clardy, Feb 23 2013

Status

approved