A374105 - OEIS

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

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OFFSET

1,1

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.

LINKS

EXAMPLE

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

PROG

(PARI) isok(k)={k%3 && ispseudoprime((9^k + 3^k + 1)/13)}

{ for(k=1, 2000, if(isok(k), print1(k, ", "))) }

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

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

STATUS

approved