cp's OEIS Frontend

A124989 Primes of the form 10*k + 9 generated recursively. Initial prime is 19. General term is a(n) = Min_{p is prime; p divides 100*Q^2 - 5; p == 9 (mod 10)}, where Q is the product of previous terms in the sequence.

%I A124989 #12 Aug 07 2022 02:06:43
%S A124989 19,7219,462739,509,129229,295380580489,9653956849,149,
%T A124989 110212292237172705230749846071050188009093377022084806290042881946231583507557298889,
%U A124989 157881589,60397967745386189,1429,79
%N A124989 Primes of the form 10*k + 9 generated recursively. Initial prime is 19. General term is a(n) = Min_{p is prime; p divides 100*Q^2 - 5; p == 9 (mod 10)}, where Q is the product of previous terms in the sequence.
%C A124989 100Q^2-5 always has a prime divisor congruent to 9 modulo 10.
%H A124989 Robert Price, <a href="/A124989/b124989.txt">Table of n, a(n) for n = 1..14</a>
%e A124989 a(3) = 462739 is the smallest prime divisor congruent to 9 mod 10 of 100Q^2-5 = 1881313992095 = 5 * 462739 * 813121, where Q = 19 * 7219.
%t A124989 a={19}; q=1;
%t A124989 For[n=2,n<=6,n++,
%t A124989     q=q*Last[a];
%t A124989     AppendTo[a,Min[Select[FactorInteger[100*q^2-5][[All,1]],Mod[#,10]==9&]]];
%t A124989     ];
%t A124989 a (* _Robert Price_, Jul 18 2015 *)
%Y A124989 Cf. A000945, A030433, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K A124989 nonn
%O A124989 1,1
%A A124989 _Nick Hobson_, Nov 18 2006