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A124990
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Primes of the form 12k+1 generated recursively. Initial prime is 13. General term is a(n)=Min {p is prime; p divides Q^4-Q^2+1}, where Q is the product of previous terms in the sequence.
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2
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OFFSET
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1,1
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COMMENTS
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All prime divisors of Q^4 - Q^2 + 1 are congruent to 1 modulo 12.
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REFERENCES
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K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, NY, Second Edition (1990), p. 63.
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LINKS
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EXAMPLE
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a(3) = 128758492789 is the smallest prime divisor of Q^4 - Q^2 + 1 = 18561733755472408508281 = 128758492789 * 144159296629, where Q = 13 * 28393.
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MATHEMATICA
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a = {13}; q = 1;
For[n = 2, n ≤ 8, n++,
q = q*Last[a];
AppendTo[a, Min[Select[FactorInteger[q^4 - q^2 + 1][[All, 1]],
Mod[#, 12] == 1 &]]];
];
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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