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%I #29 Sep 13 2024 08:43:05
%S 2,5,7,11,541,1583,2713,2963,13831,22349,22669,23833,57287
%N Numbers k such that (9^k + 3^k + 1)/13 is prime.
%C Conjecturally all terms are prime. There are no composite terms < 24000.
%C 57287 will be the next term if there are no composite terms below. There are no other prime terms < 100000.
%C Terms > 2963 correspond to probable primes.
%e 5 is a term because (9^5 + 3^5 + 1)/13 = 4561 is prime.
%o (PARI) isok(k)={k%3 && ispseudoprime((9^k + 3^k + 1)/13)}
%o { for(k=1, 2000, if(isok(k), print1(k, ", "))) }
%Y Cf. A028491, A359436.
%K nonn,more
%O 1,1
%A _Aurelien Gibier_, Jun 29 2024
%E a(13) confirmed by _Michael S. Branicky_, Sep 13 2024