A125043 - OEIS

A125043

Primes of the form 18k+1 generated recursively. Initial prime is 19. General term is a(n) = Min {p is prime; p divides (R^9 - 1)/(R^3 - 1); p == 1 (mod 9)}, where Q is the product of previous terms in the sequence and R = 3*Q.

%I #15 Feb 11 2024 14:19:28

%S 19,20593,163,8321800321246060993879,9002496685879,

%T 9736549840211105800055992105260095004185761,1117,48871,37,109,

%U 2072647,811,2647,22934467,73,10715232331,4861,127,883,699733,19918378819555761579853986597710971

%N Primes of the form 18k+1 generated recursively. Initial prime is 19. General term is a(n) = Min {p is prime; p divides (R^9 - 1)/(R^3 - 1); p == 1 (mod 9)}, where Q is the product of previous terms in the sequence and R = 3*Q.

%C All prime divisors of (R^9 - 1)/(R^3 - 1) different from 3 are congruent to 1 modulo 18.

%D M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), p. 209.

%e a(3) = 163 is the smallest prime divisor congruent to 1 mod 18 of (R^9-1)/(R^3-1) = 2615573032645879161713714169238484203 = 163 * 88080931 * 161773561 * 1126133310262611691, where Q = 19 * 20593 and R = 3*Q.

%Y Cf. A000945, A061237, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

%K more,nonn

%O 1,1

%A _Nick Hobson_, Nov 18 2006

%E More terms from _Sean A. Irvine_, Feb 02 2012