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A176007
Numbers n such that 3^(2n-1)-3^n+1 is prime.
1
2, 5, 6, 97, 120, 330, 355, 552, 1015, 4525, 5227
OFFSET
1,1
COMMENTS
3^(2n-1)-3^n+1 is an Aurifeuillean factor of 3^(6n-3)+1, sometimes written as L(3,6n-3).
h=2n-1 must be a power of 3 or a prime congruent to 1 or 11 (mod 12). For all other h, there are algebraic factorizations: for prime p>3, L(3,pq) are divisible by L(3,p) or M(3,p).
No other terms a(n)<55800 exist.
LINKS
Eric Weisstein's World of Mathematics, Aurifeuillean Factorization.
EXAMPLE
For n = 2 the a(2) = 5, because 3^9-3^5+1 = 19441 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
Cf. A176008 for Aurifeuillean co-factor M(3, 6n-3).
Sequence in context: A219117 A111190 A244434 * A009376 A231364 A025123
KEYWORD
hard,more,nonn
AUTHOR
Serge Batalov, Apr 09 2010
STATUS
approved