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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

%I

%S 17,47441,5136468762577,1217,2413992194819190142614641,113,52654897,

%T 241,5310928841473,673

%N 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.

%C All prime divisors of (2Q)^8 + 1 are congruent to 1 modulo 16.

%D G. A. Jones and J. M. Jones, Elementary Number Theory, Springer-Verlag, NY, (1998), p. 271.

%H N. Hobson, <a href="http://www.qbyte.org/puzzles/">Home page (listed in lieu of email address)</a>

%e a(3) = 5136468762577 is the smallest prime divisor of (2Q)^8 + 1 = 45820731194492299767895461612240999140120699535617 = 5136468762577 * 33000748370307713 * 270317134666005456817, where Q = 17 * 47441.

%t a = {17}; q = 1;

%t For[n = 2, n <= 3, n++,

%t q = q*Last[a];

%t AppendTo[a, Min[Select[FactorInteger[(2*q)^8 + 1][[All, 1]],

%t Mod[#, 16] == 1 &]]];

%t ];

%t a (* _Robert Price_, Jul 14 2015 *)

%Y Cf. A000945, A094407, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

%K more,nonn

%O 1,1

%A Nick Hobson, Nov 18 2006

%E a(5)..a(10) from _Max Alekseyev_, Oct 18 2008

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)