A124989 - OEIS

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 #12 Aug 07 2022 02:06:43

%S 19,7219,462739,509,129229,295380580489,9653956849,149,

%T 110212292237172705230749846071050188009093377022084806290042881946231583507557298889,

%U 157881589,60397967745386189,1429,79

%N 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 100Q^2-5 always has a prime divisor congruent to 9 modulo 10.

%H Robert Price, <a href="/A124989/b124989.txt">Table of n, a(n) for n = 1..14</a>

%e 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 a={19}; q=1;

%t For[n=2,n<=6,n++,

%t q=q*Last[a];

%t AppendTo[a,Min[Select[FactorInteger[100*q^2-5][[All,1]],Mod[#,10]==9&]]];

%t ];

%t a (* _Robert Price_, Jul 18 2015 *)

%Y Cf. A000945, A030433, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

%K nonn

%O 1,1

%A _Nick Hobson_, Nov 18 2006