cp's OEIS Frontend

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.

%I A125038 #23 Feb 11 2024 14:19:49
%S A125038 103,307,9929,187095201191,76943,37061,137,5615258941637,302125531,
%T A125038 18089,613,409,9419,193189
%N 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.
%C A125038 All prime divisors of (R^17 - 1)/(R - 1) different from 17 are congruent to 1 modulo 34.
%D A125038 M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), pp. 208-209.
%e A125038 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.
%t A125038 a={103}; q=1;
%t A125038 For[n=2,n<=5,n++,
%t A125038     q=q*Last[a]; r=17*q;
%t A125038     AppendTo[a,Min[Select[FactorInteger[(r^17-1)/(r-1)][[All,1]],Mod[#,34]==1 &]]];
%t A125038     ];
%t A125038 a (* _Robert Price_, Jul 14 2015 *)
%Y A125038 Cf. A000945, A057204-A057208, A051308-A051335, A124984-A125038, A125037-A125045.
%K A125038 more,nonn
%O A125038 1,1
%A A125038 _Nick Hobson_, Nov 18 2006
%E A125038 a(9)-a(14) from _Sean A. Irvine_, Jun 27 2011