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%I #13 Feb 11 2024 14:19:32
%S 17,47441,33000748370307713,21377
%N Primes of the form 48k+17 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^8 + 1; Mod[p,48]=17}, 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.
%C At least one prime divisor of (2Q)^8 + 1 is congruent to 2 modulo 3 and hence to 17 modulo 48.
%C The first two terms are the same as those of A125040.
%D G. A. Jones and J. M. Jones, Elementary Number Theory, Springer-Verlag, NY, (1998), p. 271.
%e a(3) = 33000748370307713 is the smallest prime divisor congruent to 17 mod 48 of (2Q)^8 + 1 = 45820731194492299767895461612240999140120699535617 = 5136468762577 * 33000748370307713 * 270317134666005456817, where Q = 17 * 47441.
%t a = {17}; q = 1;
%t For[n = 2, n ≤ 2, n++,
%t q = q*Last[a];
%t AppendTo[a, Min[Select[FactorInteger[(2*q)^8 + 1][[All, 1]],
%t Mod[#, 48] \[Equal] 17 &]]];
%t ];
%t a (* _Robert Price_, Jul 14 2015 *)
%Y Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K more,nonn
%O 1,1
%A _Nick Hobson_, Nov 18 2006
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