A125037 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.

53, 11462027512399586179504472990060461, 25793, 178907, 131, 5669, 3511, 157, 59021, 13070705295701, 547, 79, 424361132339, 126146525792794964042953901, 5889547, 521, 1301, 6249393047, 9829, 2549, 298378081, 29379481, 56993, 1093, 26729

Offset: 1

Author

Nick Hobson, Nov 18 2006

Keywords

• nonn

Comments

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

Examples

			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.
		

References

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

Crossrefs

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

Programs

Mathematica

a={53}; q=1;
For[n=2,n<=5,n++,
    q=q*Last[a]; r=13*q;
    AppendTo[a,Min[Select[FactorInteger[(r^13-1)/(r-1)][[All,1]],Mod[#,26]==1 &]]];
    ];
a (* Robert Price, Jul 16 2015 *)

Extensions

More terms from Sean A. Irvine, Jun 24 2011