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A125041
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Primes of the form 24k+17 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^4 + 1; Mod[p,24]=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)^4 + 1 are congruent to 1 modulo 8.
At least one prime divisor of (2Q)^4 + 1 is congruent to 2 modulo 3 and hence to 17 modulo 24.
The first four terms are the same as those of A125039.
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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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Table of n, a(n) for n=1..4.
N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
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a(3) = 4261668267710686591310687815697 is the smallest prime
divisor congruent to 17 mod 24 of (2Q)^4 + 1 =
4261668267710686591310687815697, where Q = 17 * 1336337.
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CROSSREFS
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Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A177816 A130653 A125039 * A013806 A147671 A104536
Adjacent sequences: A125038 A125039 A125040 * A125042 A125043 A125044
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KEYWORD
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more,nonn
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AUTHOR
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Nick Hobson Nov 18 2006
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STATUS
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approved
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