|
%I #17 Feb 11 2024 17:11:50
%S 7,199,7761799,487,67,103,1482549740515442455520791,31,139,787,19,
%T 39266047,1955959,50650885759,367,185767,62168707
%N Primes of the form 12k+7 generated recursively. Initial prime is 7. General term is a(n)=Min {p is prime; p divides 3+4Q^2; Mod[p,12]=7}, where Q is the product of previous terms in the sequence.
%C All prime divisors of 3+4Q^2 are congruent to 1 modulo 6.
%C At least one prime divisor of 3+4Q^2 is congruent to 3 modulo 4 and hence to 7 modulo 12.
%C The first six terms are the same as those of A057204.
%H Tyler Busby, <a href="/A124988/b124988.txt">Table of n, a(n) for n = 1..21</a>
%e a(3) = 1482549740515442455520791 is the smallest prime divisor congruent to 7 mod 12 of 3+4Q^2 = 5281642303363312989311974746340327 = 3562539697 * 1482549740515442455520791, where Q = 7 * 199 * 7761799 * 487 * 67 * 103.
%t a={7}; q=1;
%t For[n=2,n<=7,n++,
%t q=q*Last[a];
%t AppendTo[a,Min[Select[FactorInteger[4*q^2+3][[All,1]],Mod[#,12]==7 &]]];
%t ];
%t a (* _Robert Price_, Jul 15 2015 *)
%Y Cf. A000945, A068229, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K nonn
%O 1,1
%A _Nick Hobson_, Nov 18 2006
|
