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Search: id:A125042
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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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1
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OFFSET
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1,1
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COMMENT
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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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N. Hobson, Home page (listed in lieu of email address)
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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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CROSSREFS
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Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A068733 A066161 A125040 this_sequence A138942 A075902 A013760
Adjacent sequences: A125039 A125040 A125041 this_sequence A125043 A125044 A125045
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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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