A124992 Primes of the form 14k+1 generated recursively. Initial prime is 29. General term is a(n)=Min {p is prime; p divides (R^7 - 1)/(R - 1); Mod[p,7]=1}, where Q is the product of previous terms in the sequence and R = 7Q.

29, 70326806362093, 43, 127, 59221, 113, 32411, 71, 4957, 74509, 4271, 19013, 239, 2003, 463, 421, 613575503674084673, 32089, 211, 54601, 3109

Offset: 1

Author

Nick Hobson, Nov 18 2006

Keywords

• more
• nonn

Comments

All prime divisors of (R^7 - 1)/(R - 1) different from 7 are congruent to 1 modulo 14.

Examples

			a(3) = 43 is the smallest prime divisor congruent to 1 mod 14 of (R^7 - 1)/(R-1) =
8466454975669959912248567627122565866080343755024168315838344565727361366925647440393797835238961
= 43 * 10781 * 391441 * 428597443 * 11795628769 * 408944901028399 * 22566921596365593811470735460776534824496318810581339, where Q = 29 * 70326806362093 and R = 7Q.
		

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={29}; q=1;
For[n=2,n<=3,n++,
    q=q*Last[a]; r=7*q;
    AppendTo[a,Min[Select[FactorInteger[(r^7-1)/(r-1)][[All,1]],Mod[#,14]==1 &]]];
    ];
a (* Robert Price, Jul 14 2015 *)