A125038 Primes of the form 34k+1 generated recursively. Initial prime is 103. General term is a(n) = Min {p is prime; p divides (R^17 - 1)/(R - 1); p == 1 (mod 17)}, where Q is the product of previous terms in the sequence and R = 17*Q.

103, 307, 9929, 187095201191, 76943, 37061, 137, 5615258941637, 302125531, 18089, 613, 409, 9419, 193189

Offset

1,1

Comments

All prime divisors of (R^17 - 1)/(R - 1) different from 17 are congruent to 1 modulo 34.

References

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

Links

Table of n, a(n) for n=1..14.

Example

a(2) = 307 is the smallest prime divisor congruent to 1 mod 34 of (R^17 - 1)/(R-1) = 7813154903878257490980895975711871949096304270238017 = 307 * 326669135226428664734261 * 77907623430368753779713071, where Q = 103 and R = 17*Q.

Mathematica

a={103}; q=1;
For[n=2, n<=5, n++,
    q=q*Last[a]; r=17*q;
    AppendTo[a, Min[Select[FactorInteger[(r^17-1)/(r-1)][[All, 1]], Mod[#, 34]==1 &]]];
    ];
a (* Robert Price, Jul 14 2015 *)

Crossrefs

Cf. A000945, A057204-A057208, A051308-A051335, A124984-A125038, A125037-A125045.

Sequence in context: A023352 A142476 A136067 * A142531 A142693 A142840

Adjacent sequences: A125035 A125036 A125037 * A125039 A125040 A125041

Keyword

more,nonn

Author

Nick Hobson, Nov 18 2006

Extensions

a(9)-a(14) from Sean A. Irvine, Jun 27 2011

Status

approved