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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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19, 20593, 163, 8321800321246060993879, 9002496685879, 9736549840211105800055992105260095004185761, 1117, 48871, 37, 109, 2072647, 811, 2647, 22934467, 73, 10715232331, 4861, 127, 883, 699733, 19918378819555761579853986597710971
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All prime divisors of (R^9 - 1)/(R^3 - 1) different from 3 are congruent to 1 modulo 18.
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REFERENCES
| M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), p. 209.
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LINKS
| N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
| 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
| Cf. A000945, A061237, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A110392 A107100 A203581 * A013528 A172762 A203703
Adjacent sequences: A125040 A125041 A125042 * A125044 A125045 A125046
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KEYWORD
| more,nonn
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AUTHOR
| Nick Hobson Nov 18 2006
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EXTENSIONS
| More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Feb 02 2012
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