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 A125041 Primes of the form 24k+17 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^4 + 1; Mod[p,24]=17}, where Q is the product of previous terms in the sequence. 0
 17, 1336337, 4261668267710686591310687815697, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All prime divisors of (2Q)^4 + 1 are congruent to 1 modulo 8. At least one prime divisor of (2Q)^4 + 1 is congruent to 2 modulo 3 and hence to 17 modulo 24. The first four terms are the same as those of A125039. REFERENCES G. A. Jones and J. M. Jones, Elementary Number Theory, Springer-Verlag, NY, (1998), p. 271. LINKS N. Hobson, Home page (listed in lieu of email address) EXAMPLE a(3) = 4261668267710686591310687815697 is the smallest prime divisor congruent to 17 mod 24 of (2Q)^4 + 1 = 4261668267710686591310687815697, where Q = 17 * 1336337. CROSSREFS Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045. Sequence in context: A177816 A130653 A125039 * A013806 A147671 A104536 Adjacent sequences:  A125038 A125039 A125040 * A125042 A125043 A125044 KEYWORD more,nonn AUTHOR Nick Hobson Nov 18 2006 STATUS approved

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