A125037 - OEIS

%I #17 Feb 11 2024 14:20:08

%S 53,11462027512399586179504472990060461,25793,178907,131,5669,3511,

%T 157,59021,13070705295701,547,79,424361132339,

%U 126146525792794964042953901,5889547,521,1301,6249393047,9829,2549,298378081,29379481,56993,1093,26729

%N Primes of the form 26k+1 generated recursively. Initial prime is 53. General term is a(n) = Min {p is prime; p divides (R^13 - 1)/(R - 1); p == 1 (mod 13)}, where Q is the product of previous terms in the sequence and R = 13*Q.

%C All prime divisors of (R^13 - 1)/(R - 1) different from 13 are congruent to 1 modulo 26.

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

%e a(2) = 11462027512399586179504472990060461 is the smallest prime divisor congruent to 1 mod 26 of (R^13 - 1)/(R - 1) = 11462027512399586179504472990060461, where Q = 53 and R = 13*Q.

%t a={53}; q=1;

%t For[n=2,n<=5,n++,

%t     q=q*Last[a]; r=13*q;

%t     AppendTo[a,Min[Select[FactorInteger[(r^13-1)/(r-1)][[All,1]],Mod[#,26]==1 &]]];

%t     ];

%t a (* _Robert Price_, Jul 16 2015 *)

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

%K nonn

%O 1,1

%A _Nick Hobson_, Nov 18 2006

%E More terms from _Sean A. Irvine_, Jun 24 2011