A174326 Exactly one of 3^n +- 2^n is prime.

0, 1, 3, 4, 5, 17, 29, 31, 53, 59, 101, 277, 647, 1061, 2381, 2833, 3613, 3853, 3929, 5297, 7417, 90217, 122219, 173191, 256199, 336353, 485977, 591827, 1059503

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 15 2010

Keywords

• nonn

Comments

Either (but not both) of 3^n - 2^n and 3^n + 2^n is prime. - Harvey P. Dale, Sep 16 2016

If 3^n + 2^n is prime then n must be a power of 2, and 3^n + 2^n is a generalized Fermat prime. It is conjectured that 3^n + 2^n is prime only for n=1,2,4: see A082101. - Robert Israel, Mar 15 2017, edited May 18 2017.

Examples

			a(1)=0 because 3^0 - 2^0 = 0 = nonprime and 3^0 + 2^0 = 2 = prime;
a(2)=1 because 3^1 - 2^1 = 1 = nonprime and 3^1 + 2^1 = 5 = prime;
a(3)=3 because 3^3 - 2^3 = 19 = prime and 3^3 + 2^3 = 35 = nonprime.
		

Crossrefs

Cf. A283653, A082101, A057468.

Programs

Mathematica

epQ[n_]:=Module[{a=3^n,b=2^n},Sort[PrimeQ[{a+b,a-b}]]=={False,True}]; Select[Range[0,4000],epQ] (* Harvey P. Dale, Sep 16 2016 *)

PARI

is(n)=isprime(3^n+2^n)+isprime(3^n-2^n)==1 \\ Charles R Greathouse IV, Mar 19 2017

Extensions

9 and 11 removed by R. J. Mathar, Mar 29 2010

More terms from Harvey P. Dale, Sep 16 2016

a(20) from Robert G. Wilson v, Mar 15 2017

a(21) to a(29) (using data from A057468) from Robert Israel, May 18 2017