

A174326


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


1



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
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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



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, ab}]]=={False, True}]; Select[Range[0, 4000], epQ] (* Harvey P. Dale, Sep 16 2016 *)


PROG



CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



