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Search: id:A124990
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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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+0
2
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OFFSET
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1,1
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COMMENT
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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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N. Hobson, Home page (listed in lieu of email address)
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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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CROSSREFS
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Cf. A000945, A068228, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A098562 A123921 A145716 this_sequence A013752 A076811 A048917
Adjacent sequences: A124987 A124988 A124989 this_sequence A124991 A124992 A124993
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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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