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A125042
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Primes of the form 48k+17 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^8 + 1; Mod[p,48]=17}, where Q is the product of previous terms in the sequence.
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0
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OFFSET
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1,1
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COMMENTS
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All prime divisors of (2Q)^8 + 1 are congruent to 1 modulo 16.
At least one prime divisor of (2Q)^8 + 1 is congruent to 2 modulo 3 and hence to 17 modulo 48.
The first two terms are the same as those of A125040.
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REFERENCES
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G. A. Jones and J. M. Jones, Elementary Number Theory, Springer-Verlag, NY, (1998), p. 271.
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LINKS
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EXAMPLE
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a(3) = 33000748370307713 is the smallest prime divisor congruent to 17 mod 48 of (2Q)^8 + 1 = 45820731194492299767895461612240999140120699535617 = 5136468762577 * 33000748370307713 * 270317134666005456817, where Q = 17 * 47441.
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MATHEMATICA
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a = {17}; q = 1;
For[n = 2, n ≤ 2, n++,
q = q*Last[a];
AppendTo[a, Min[Select[FactorInteger[(2*q)^8 + 1][[All, 1]],
Mod[#, 48] \[Equal] 17 &]]];
];
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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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STATUS
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approved
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