cp's OEIS Frontend

A125044 Primes of the form 54k+1 generated recursively. Initial prime is 109. General term is a(n) = Min {p is prime; p divides (R^27 - 1)/(R^9 - 1); p == 1 (mod 27)}, where Q is the product of previous terms in the sequence and R = 3*Q.

%I A125044 #16 Feb 11 2024 14:19:23
%S A125044 109,50221,379,5077,2527181639419400128997560106426867837203,112807,
%T A125044 2094067,1567,9325207,370603,67447,27978113462777647321591,1012771,
%U A125044 163,396577,7096357,3511,3673,541,389287,1999,68979565009,649108891
%N A125044 Primes of the form 54k+1 generated recursively. Initial prime is 109. General term is a(n) = Min {p is prime; p divides (R^27 - 1)/(R^9 - 1); p == 1 (mod 27)}, where Q is the product of previous terms in the sequence and R = 3*Q.
%C A125044 All prime divisors of (R^27 - 1)/(R^9 - 1) different from 3 are congruent to 1 modulo 54.
%D A125044 M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), p. 209.
%e A125044 a(2) = 50221 is the smallest prime divisor congruent to 1 mod 54 of
%e A125044   (R^27-1)/(R^9- 1) = 1827509098737085519727094436535854935801097657 = 50221 * 106219 * 342587871163695447795790279515751543, where Q = 109 and R = 3*Q.
%Y A125044 Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K A125044 nonn
%O A125044 1,1
%A A125044 _Nick Hobson_, Nov 18 2006
%E A125044 More terms from _Sean A. Irvine_, Dec 11 2011