A074326 Numbers n such that difference between (1+2^n)-th and (2^n)-th primes is 2.

1, 6, 8, 9, 17, 23, 27, 39, 48

Offset: 1

Author

Labos Elemer, Aug 21 2002

Keywords

• more
• nonn

Examples

			n=39: 2^39=549755813888, prime(549755813889) = 16149760533343, prime(549755813888) = 16149760533341, difference=2, just twin primes.
		

Crossrefs

Cf. A029707, A051439, A033844, A073798, A000079.

Programs

Mathematica

s=0; Do[s=Prime[1+2^n]-Prime[2^n]; If[s==2, Print[{n, Prime[2^n]}]], {n, 1, 40}]
diffQ[n_]:=Module[{prn=Prime[2^n]},NextPrime[prn]-prn==2]; Select[ Range[ 40],diffQ] (* Harvey P. Dale, Aug 21 2014 *)

Formula

Solutions to A051439(x) - A033844(x) = 2,

Extensions

a(9) from Chai Wah Wu, Feb 28 2019