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A125037
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Primes of the form 26k+1 generated recursively. Initial prime is 53. General term is a(n)=Min {p is prime; p divides (R^13 - 1)/(R - 1); Mod[p,13]=1}, where Q is the product of previous terms in the sequence and R = 13Q.
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19
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53, 11462027512399586179504472990060461, 25793, 178907, 131, 5669, 3511, 157, 59021, 13070705295701, 547, 79, 424361132339, 126146525792794964042953901, 5889547, 521, 1301, 6249393047, 9829, 2549, 298378081, 29379481, 56993, 1093, 26729
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All prime divisors of (R^13 - 1)/(R - 1) different from 13 are congruent to 1 modulo 26.
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REFERENCES
| M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), pp. 208-209.
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LINKS
| N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
| a(2) = 11462027512399586179504472990060461 is the smallest
prime divisor congruent to 1 mod 26 of (R^13 - 1)/(R - 1) =
11462027512399586179504472990060461, where Q = 53 and R = 13Q.
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CROSSREFS
| Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A183793 A145332 A087530 * A101365 A022080 A033688
Adjacent sequences: A125034 A125035 A125036 * A125038 A125039 A125040
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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), Jun 24 2011
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