cp's OEIS Frontend

A125041 Primes of the form 24k+17 generated recursively. Initial prime is 17. General term is a(n) = Min {p is prime; p divides (2Q)^4 + 1; p == 17 (mod 24)}, where Q is the product of previous terms in the sequence.

%I A125041 #19 Feb 11 2024 14:19:35
%S A125041 17,1336337,4261668267710686591310687815697,41,
%T A125041 904641301321079897900944986453955254215268639579197293450763646548520041534444726724543203327659858344185865089,
%U A125041 3449,18701609,8009,38599161306788868932168755721,857,130073,1433,113,809,18954775793
%N A125041 Primes of the form 24k+17 generated recursively. Initial prime is 17. General term is a(n) = Min {p is prime; p divides (2Q)^4 + 1; p == 17 (mod 24)}, where Q is the product of previous terms in the sequence.
%C A125041 All prime divisors of (2Q)^4 + 1 are congruent to 1 modulo 8.
%C A125041 At least one prime divisor of (2Q)^4 + 1 is congruent to 2 modulo 3 and hence to 17 modulo 24.
%C A125041 The first four terms are the same as those of A125039.
%D A125041 G. A. Jones and J. M. Jones, Elementary Number Theory, Springer-Verlag, NY, (1998), p. 271.
%H A125041 Sean A. Irvine, <a href="/A125041/b125041.txt">Table of n, a(n) for n = 1..20</a>
%e A125041 a(3) = 4261668267710686591310687815697 is the smallest prime divisor congruent to 17 mod 24 of (2Q)^4 + 1 = 4261668267710686591310687815697, where Q = 17 * 1336337.
%Y A125041 Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K A125041 nonn
%O A125041 1,1
%A A125041 _Nick Hobson_, Nov 18 2006
%E A125041 More terms from _Sean A. Irvine_, Jun 09 2015