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.

11, 211, 1031, 22741, 41, 15487770335331184216023237599647357572461782407557681, 311, 61, 55172461, 3541, 1381, 2851, 19841, 151, 9033671, 456802301, 1720715817015281, 19001, 71

Offset: 1

Author

Nick Hobson, Nov 18 2006

Keywords

• nonn

Comments

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

Examples

			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.
		

References

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

Links

• Max Alekseyev, Table of n, a(n) for n=1..34

Crossrefs

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

Programs

Mathematica

a={11}; q=1;
For[n=2,n<=6,n++,
    q=q*Last[a]; r=5*q;
    AppendTo[a,Min[Select[FactorInteger[(r^5-1)/(r-1)][[All,1]],Mod[#,10]==1&]]];
    ];
a (* Robert Price, Jul 14 2015 *)

Extensions

a(20)..a(34) in b-file from Max Alekseyev, Oct 23 2008