A124993 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.

23, 4847239, 2971, 3936923, 9461, 1453, 331, 81373909, 89, 920771904664817214817542307, 353, 401743, 17088192002665532981, 11617

Offset: 1

Author

Nick Hobson, Nov 18 2006

Keywords

• more
• nonn

Comments

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

Examples

			a(3) = 2971 is the smallest prime divisor congruent to 1 mod 22 of (R^11-1)/(R-1) =
7693953366218628230903493622259922359469805176129784863956847906415055607909988155588181877
= 2971 * 357405886421 * 914268562437006833738317047149 * 7925221522553970071463867283158786415606996703, where Q = 23 * 4847239, and R = 11*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={23}; q=1;
For[n=2,n<=2,n++,
    q=q*Last[a]; r=11*q;
    AppendTo[a,Min[Select[FactorInteger[(r^11-1)/(r-1)][[All,1]],Mod[#,11]==1 &]]];
    ];
a (* Robert Price, Jul 14 2015 *)

Extensions

More terms from Max Alekseyev, May 29 2009