

A220746


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


2




OFFSET

1,1


LINKS



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^n10, 2^n], Range[ 2^n, 2^n+10]}], AllTrue[ #, PrimeQ]&], {n, 3, 1000}], 1][[;; , 1]]] (* Harvey P. Dale, Feb 19 2023 *)


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. In this example 3 also works.
gap:=10;
start:=Ilog2(gap)+1;
for i:= start to 1000 do
powerof2:=2^i;
for k:=powerof2gap+1 to powerof21 by 2 do
if (IsPrime(k) and IsPrime(k+gap)) then k;
end if;
end for;
end for;
(PARI) print1(3); for(n=4, 500, forprime(p=2^n9, 2^n1, if(isprime(p+10), print1(", "p)))) \\ Charles R Greathouse IV, Feb 20 2013


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



