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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.

%I A125040 #17 Feb 11 2024 14:19:40
%S A125040 17,47441,5136468762577,1217,2413992194819190142614641,113,52654897,
%T A125040 241,5310928841473,673
%N 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.
%C A125040 All prime divisors of (2Q)^8 + 1 are congruent to 1 modulo 16.
%D A125040 G. A. Jones and J. M. Jones, Elementary Number Theory, Springer-Verlag, NY, (1998), p. 271.
%e A125040 a(3) = 5136468762577 is the smallest prime divisor of (2Q)^8 + 1 = 45820731194492299767895461612240999140120699535617 = 5136468762577 * 33000748370307713 * 270317134666005456817, where Q = 17 * 47441.
%t A125040 a = {17}; q = 1;
%t A125040 For[n = 2, n <= 3, n++,
%t A125040     q = q*Last[a];
%t A125040     AppendTo[a, Min[Select[FactorInteger[(2*q)^8 + 1][[All, 1]],
%t A125040     Mod[#, 16] == 1 &]]];
%t A125040     ];
%t A125040 a (* _Robert Price_, Jul 14 2015 *)
%Y A125040 Cf. A000945, A094407, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K A125040 more,nonn
%O A125040 1,1
%A A125040 _Nick Hobson_, Nov 18 2006
%E A125040 a(5)-a(10) from _Max Alekseyev_, Oct 18 2008