%I #24 Feb 11 2024 14:20:12

%S 23,4847239,2971,3936923,9461,1453,331,81373909,89,

%T 920771904664817214817542307,353,401743,17088192002665532981,11617

%N Primes of the form 22k+1 generated recursively. Initial prime is 23. General term is a(n) = Min {p is prime; p divides (R^11 - 1)/(R - 1); p == 1 (mod 11)}, where Q is the product of previous terms in the sequence and R = 11*Q.

%C All prime divisors of (R^11 - 1)/(R - 1) different from 11 are congruent to 1 modulo 22.

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

%e a(3) = 2971 is the smallest prime divisor congruent to 1 mod 22 of (R^11-1)/(R-1) =

%e 7693953366218628230903493622259922359469805176129784863956847906415055607909988155588181877

%e = 2971 * 357405886421 * 914268562437006833738317047149 * 7925221522553970071463867283158786415606996703, where Q = 23 * 4847239, and R = 11*Q.

%t a={23}; q=1;

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

%t q=q*Last[a]; r=11*q;

%t AppendTo[a,Min[Select[FactorInteger[(r^11-1)/(r-1)][[All,1]],Mod[#,11]==1 &]]];

%t ];

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

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

%K more,nonn

%O 1,1

%A _Nick Hobson_, Nov 18 2006

%E More terms from _Max Alekseyev_, May 29 2009