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%I #16 Feb 11 2024 14:19:45
%S 17,1336337,4261668267710686591310687815697,41,
%T 4390937134822286389262585915435960722186022220433,241,1553,
%U 243537789182873,97,27673,4289,457,137201,73,337,569891669978849,617,1697,65089,1609,761
%N Primes of the form 8k+1 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^4 + 1}, where Q is the product of previous terms in the sequence.
%C All prime divisors of (2Q)^4 + 1 are congruent to 1 modulo 8.
%D G. A. Jones and J. M. Jones, Elementary Number Theory, Springer-Verlag, NY, (1998), p. 271.
%H Sean A. Irvine, <a href="/A125039/b125039.txt">Table of n, a(n) for n = 1..29</a>
%e a(3) = 4261668267710686591310687815697 is the smallest prime divisor of (2Q)^4 + 1 = 4261668267710686591310687815697, where Q = 17 * 1336337.
%Y Cf. A000945, A007519, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K nonn
%O 1,1
%A _Nick Hobson_, Nov 18 2006
%E More terms from _Sean A. Irvine_, Apr 09 2015