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URL: https://oeis.org/A089213

⇱ A089213 - OEIS

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A089213
Primes p such that either 3^p-2 or 3^p+2 is prime or both are.
0
2, 3, 5, 37, 41, 139, 317, 541, 2521
OFFSET
1,1
COMMENTS
At p = 2, 3, 139, 3^p + 2 is prime, while at p = 2, 5, 37, 41, 317, 541, 2521 3^p - 2 is prime.
a(10) > 2*10^5. - Robert Price, Nov 20 2013
EXAMPLE
2 is in the sequence because both 3^2 - 2 = 7 and 3^2 + 2 = 11 are primes.
3 is in the sequence because 3^3 + 2 = 29 is a prime (though 3^3 - 2 = 25 = 5^2).
5 is in the sequence because 3^5 - 2 = 241 is a prime (though 3^5 + 2 = 245 = 5 * 7^2).
MATHEMATICA
Select[Prime[Range[100]], PrimeQ[3^# - 2] || PrimeQ[3^# + 2] &] (* Alonso del Arte, Nov 20 2013 *)
Select[Prime[Range[400]], AnyTrue[3^#+{2, -2}, PrimeQ]&] (* Harvey P. Dale, Aug 03 2025 *)
CROSSREFS
Sequence in context: A362640 A261130 A271387 * A029499 A347720 A128026
KEYWORD
nonn,more,hard
AUTHOR
Herman H. Rosenfeld (herm3(AT)pacbell.net), Dec 20 2003
EXTENSIONS
Edited by Zak Seidov, Aug 08 2006
Definition clarified by Harvey P. Dale, Aug 03 2025
STATUS
approved