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

1,3

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.

Links

Table of n, a(n) for n=1..29.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A283653, A082101, A057468.

Sequence in context: A298225 A278919 A173061 * A224890 A263810 A249541

Adjacent sequences: A174323 A174324 A174325 * A174327 A174328 A174329

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 15 2010

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

Status

approved