A124991 - OEIS

A124991

Primes of the form 10k+1 generated recursively. Initial prime is 11. General term is a(n)=Min {p is prime; p divides (R^5 - 1)/(R - 1); Mod[p,5]=1}, where Q is the product of previous terms in the sequence and R = 5Q.

%I #20 Feb 11 2024 17:11:25

%S 11,211,1031,22741,41,

%T 15487770335331184216023237599647357572461782407557681,311,61,

%U 55172461,3541,1381,2851,19841,151,9033671,456802301,1720715817015281,19001,71

%N Primes of the form 10k+1 generated recursively. Initial prime is 11. General term is a(n)=Min {p is prime; p divides (R^5 - 1)/(R - 1); Mod[p,5]=1}, where Q is the product of previous terms in the sequence and R = 5Q.

%C All prime divisors of (R^5 - 1)/(R - 1) different from 5 are congruent to 1 modulo 10.

%D M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), pp. 208-209.

%H Max Alekseyev, <a href="/A124991/b124991.txt">Table of n, a(n) for n=1..34</a>

%e a(3) = 1031 is the smallest prime divisor congruent to 1 mod 10 of (R^5 - 1)/(R - 1) = 18139194759758381 = 1031 * 17593787351851, where Q = 11 * 211 and R = 5Q.

%t a={11}; q=1;

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

%t q=q*Last[a]; r=5*q;

%t AppendTo[a,Min[Select[FactorInteger[(r^5-1)/(r-1)][[All,1]],Mod[#,10]==1&]]];

%t ];

%t a (* _Robert Price_, Jul 14 2015 *)

%Y Cf. A000945, A030430, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

%K nonn

%O 1,1

%A _Nick Hobson_, Nov 18 2006

%E a(20)..a(34) in b-file from _Max Alekseyev_, Oct 23 2008