OFFSET
1,2
COMMENTS
3^(2n-1)+3^n+1 is an Aurifeuillean factor of 3^(6n-3)+1, sometimes written as M(3,6n-3).
h=2n-1 must be a power of 3 or a prime congruent to 5 or 7 (mod 12). For all other h, there are algebraic factorizations: for prime p>3, M(3,pq) are divisible by L(3,p) or M(3,p).
No other terms up to 41000 exist.
a(17) > 10^5. - Robert Price, Mar 20 2014
LINKS
Eric Weisstein's World of Mathematics, Aurifeuillean Factorization.
EXAMPLE
5 is a term because 3^(5*2-1) + 3^5 + 1 = 19927 is prime.
MATHEMATICA
Do[ If[ PrimeQ[3^(2*n-1)+3^n+1], Print[n]], {n, 0, 10000}]
PROG
(PARI) for(k=1, 1000, if(isprime(3^(2*k-1)+3^k+1), print(k)))
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Serge Batalov, Apr 09 2010
STATUS
approved