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 A125040 Primes of the form 16k+1 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^8 + 1}, where Q is the product of previous terms in the sequence. 1
 17, 47441, 5136468762577, 1217, 2413992194819190142614641, 113, 52654897, 241, 5310928841473, 673 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All prime divisors of (2Q)^8 + 1 are congruent to 1 modulo 16. 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) = 5136468762577 is the smallest prime divisor of (2Q)^8 + 1 = 45820731194492299767895461612240999140120699535617 = 5136468762577 * 33000748370307713 * 270317134666005456817, where Q = 17 * 47441. MATHEMATICA a = {17}; q = 1; For[n = 2, n <= 3, n++,     q = q*Last[a];     AppendTo[a, Min[Select[FactorInteger[(2*q)^8 + 1][[All, 1]],     Mod[#, 16] == 1 &]]];     ]; a (* Robert Price, Jul 14 2015 *) CROSSREFS Cf. A000945, A094407, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045. Sequence in context: A110915 A068733 A066161 * A125042 A138942 A075902 Adjacent sequences:  A125037 A125038 A125039 * A125041 A125042 A125043 KEYWORD more,nonn AUTHOR Nick Hobson, Nov 18 2006 EXTENSIONS a(5)..a(10) from Max Alekseyev, Oct 18 2008 STATUS approved

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Last modified February 26 21:51 EST 2020. Contains 332295 sequences. (Running on oeis4.)