A124987 - OEIS

%I #21 Feb 13 2024 11:34:23

%S 5,29,17,6076229,1289,78067083126343039013,521,8606045503613,15837917,

%T 1873731749,809,137,2237,17729

%N Primes of the form 12k+5 generated recursively. Initial prime is 5. General term is a(n) = Min {p is prime; p divides 4+Q^2; p == 5 (mod 12)}, where Q is the product of previous terms in the sequence.

%C Since Q is odd, all prime divisors of 4+Q^2 are congruent to 1 modulo 4.

%C At least one prime divisor of 4+Q^2 is congruent to 2 modulo 3 and hence to 5 modulo 12.

%C The first two terms are the same as those of A057208.

%H Tyler Busby, <a href="/A124987/b124987.txt">Table of n, a(n) for n = 1..15</a>

%e a(3) = 17 is the smallest prime divisor congruent to 5 mod 12 of 4+Q^2 = 21029 = 17 * 1237, where Q = 5 * 29.

%t a={5}; q=1;

%t For[n=2,n<=5,n++,

%t     q=q*Last[a];

%t     AppendTo[a,Min[Select[FactorInteger[q^2+4][[All,1]],Mod[#,12]==5 &]]];

%t     ];

%t a (* _Robert Price_, Jul 16 2015 *)

%Y Cf. A000945, A040117, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

%K more,nonn

%O 1,1

%A _Nick Hobson_, Nov 18 2006