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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 (list; graph; refs; listen; history; text; internal format)
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, 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
Sequence in context: A298225 A278919 A173061 * A224890 A263810 A249541
KEYWORD
nonn
AUTHOR
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

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Last modified April 12 11:16 EDT 2024. Contains 371633 sequences. (Running on oeis4.)