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A125044
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Primes of the form 54k+1 generated recursively. Initial prime is 109. General term is a(n)=Min {p is prime; p divides (R^27 - 1)/(R^9 - 1); Mod[p,27]=1}, where Q is the product of previous terms in the sequence and R = 3Q.
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109, 50221, 379, 5077, 2527181639419400128997560106426867837203, 112807, 2094067, 1567, 9325207, 370603, 67447, 27978113462777647321591, 1012771, 163, 396577, 7096357, 3511, 3673, 541, 389287, 1999, 68979565009, 649108891
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All prime divisors of (R^27 - 1)/(R^9 - 1) different from 3 are congruent to 1 modulo 54.
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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(2) = 50221 is the smallest prime divisor congruent to 1 mod
54 of (R^27 - 1)/(R^9 - 1) =
1827509098737085519727094436535854935801097657 = 50221 * 106219 *
342587871163695447795790279515751543, where Q = 109 and R = 3Q.
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CROSSREFS
| Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A145852 A144930 A190827 * A096209 A163597 A087303
Adjacent sequences: A125041 A125042 A125043 * A125045 A125046 A125047
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KEYWORD
| 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), Dec 11 2011
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