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%I #18 Mar 07 2017 20:59:39
%S 5,29,11,1367,13082189,89,59,29819952677,91736008068017,17,
%T 887050405736870123700827,
%U 688273423680369013308306870159348033807942418302818522537,74367405177105011,12731422703,1812053
%N Primes of the form 6k+5 generated recursively: a(1)=5; a(n) = min{p, prime; p mod 6 = 5; p | 6Q-1}, where Q is the product of all previous terms in the sequence.
%C There are infinitely many primes of the form 6k + 5, and this sequence figures in the classic proof of that fact. - _Alonso del Arte_, Mar 02 2017
%D Dirichlet, P. G. L. (1871): Vorlesungen uber Zahlentheorie. Braunschweig, Viewig, Supplement VI, 24 pages.
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, page 13.
%H Robert Price, <a href="/A057206/b057206.txt">Table of n, a(n) for n = 1..17</a>
%e a(3) = 11 is the smallest prime divisor of the form 6k + 5 of 6 * (5 * 29) - 1 = 6Q - 1 = 11 * 79 = 869.
%t primes5mod6 = {5}; q = 1;For[n = 2, n <= 10, n++, q = q * Last[ primes5mod6]; AppendTo[primes5mod6, Min[Select[FactorInteger[6 * q - 1][[All, 1]], Mod[#, 6] == 5 &]]];]; primes5mod6 (* _Robert Price_, Jul 18 2015 *)
%o (PARI) main(size)={my(v=vector(size),i,q=1,t);for(i=1,size,t=1;while(!(prime(t)%6==5&&(6*q-1)%prime(t)==0),t++);v[i]=prime(t);q*=v[i]);v;} /* _Anders Hellström_, Jul 18 2015 */
%Y Cf. A000945, A000946, A005265, A005266, A051308-A051335, A057204-A057208, A007528.
%K nonn
%O 1,1
%A _Labos Elemer_, Oct 09 2000
%E a(13)-a(17) from _Robert Price_, Jul 18 2015
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