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A176007
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Numbers n such that 3^(2n-1)-3^n+1 is prime.
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1
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2, 5, 6, 97, 120, 330, 355, 552, 1015, 4525, 5227
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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For n = 2 the a(2) = 5, because 3^9-3^5+1 = 19441 is prime.
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MATHEMATICA
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Do[ If[ PrimeQ[3^(2*n-1)-3^n+1], Print[n]], {n, 0, 10000}]
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PROG
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(PARI) for(k=1, 1000, if(isprime(3^(2*k-1)-3^k+1), print(k)))
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CROSSREFS
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Cf. A176008 for Aurifeuillean co-factor M(3, 6n-3).
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KEYWORD
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hard,more,nonn
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AUTHOR
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STATUS
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approved
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