A374105 Numbers k such that (9^k + 3^k + 1)/13 is prime.

2, 5, 7, 11, 541, 1583, 2713, 2963, 13831, 22349, 22669, 23833, 57287

Offset: 1

Author

Aurelien Gibier, Jun 29 2024

Keywords

• nonn
• more

Comments

Conjecturally all terms are prime. There are no composite terms < 24000.

57287 will be the next term if there are no composite terms below. There are no other prime terms < 100000.

Terms > 2963 correspond to probable primes.

Examples

			5 is a term because (9^5 + 3^5 + 1)/13 = 4561 is prime.
		

Crossrefs

Cf. A028491, A359436.

Programs

PARI

isok(k)={k%3 && ispseudoprime((9^k + 3^k + 1)/13)}
{ for(k=1, 2000, if(isok(k), print1(k, ", "))) }

Extensions

a(13) confirmed by Michael S. Branicky, Sep 13 2024