cp's OEIS Frontend

A124985 Primes of the form 8*k + 7 generated recursively. Initial prime is 7. General term is a(n) = Min_{p is prime; p divides 8*Q^2 - 1; p == 7 (mod 8)}, where Q is the product of the previous terms.

%I A124985 #18 Aug 15 2022 12:09:22
%S A124985 7,23,207367,1902391,167,1511,28031,79,3142977463,
%T A124985 2473230126937097422987916357409859838765327,
%U A124985 2499581669222318172005765848188928913768594409919797075052820591,223
%N A124985 Primes of the form 8*k + 7 generated recursively. Initial prime is 7. General term is a(n) = Min_{p is prime; p divides 8*Q^2 - 1; p == 7 (mod 8)}, where Q is the product of the previous terms.
%C A124985 8*Q^2 - 1 always has a prime divisor congruent to 7 modulo 8.
%D A124985 D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 182.
%e A124985 a(4) = 1902391 is the smallest prime divisor, congruent to 7 modulo 8, of 8*Q^2 - 1 = 8917046441372551 = 97 * 1902391 * 48322513, where Q = 7 * 23 * 207367.
%t A124985 a={7}; q=1;
%t A124985 For[n=2,n<=9,n++,
%t A124985     q=q*Last[a];
%t A124985     AppendTo[a,Min[Select[FactorInteger[8*q^2-1][[All,1]],Mod[#,8]==7&]]];
%t A124985     ];
%t A124985 a (* _Robert Price_, Jul 18 2015 *)
%o A124985 (PARI) main(size)={my(v=vector(size),i,q=1,t);for(i=1,size,t=1;while(!(prime(t)%8==7&&(8*q^2-1)%prime(t)==0),t++);v[i]=prime(t);q*=v[i]);v;} /* _Anders Hellström_, Jul 18 2015 */
%Y A124985 Cf. A000945, A007522, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
%K A124985 nonn
%O A124985 1,1
%A A124985 _Nick Hobson_, Nov 18 2006
%E A124985 Edited and added a(11)-a(12) by _Max Alekseyev_, May 31 2013