A176007 Numbers n such that 3^(2n-1)-3^n+1 is prime.

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

Table of n, a(n) for n=1..11.

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

Adjacent sequences: A176004 A176005 A176006 * A176008 A176009 A176010

Keyword

hard,more,nonn

Author

Serge Batalov, Apr 09 2010

Status

approved