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Search: id:A125043
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| A125043 |
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Primes of the form 18k+1 generated recursively. Initial prime is 19. General term is a(n)=Min {p is prime; p divides (R^9 - 1)/(R^3 - 1); Mod[p,9]=1}, where Q is the product of previous terms in the sequence, and R = 3Q. |
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+0
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| 19, 20593, 163, 8321800321246060993879, 9002496685879
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All prime divisors of (R^9 - 1)/(R^3 - 1) different from 3 are congruent to 1 modulo 18.
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REFERENCES
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M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), p. 209.
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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) = 163 is the smallest prime divisor congruent to 1 mod 18
of (R^9 - 1)/(R^3 - 1) = 2615573032645879161713714169238484203 = 163 *
88080931 * 161773561 * 1126133310262611691, where Q = 19 * 20593, and R =
3Q.
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CROSSREFS
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Cf. A000945, A061237, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A093400 A110392 A107100 this_sequence A068734 A034207 A098970
Adjacent sequences: A125040 A125041 A125042 this_sequence A125044 A125045 A125046
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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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