A213052 - OEIS

%I #30 Jul 13 2018 08:20:12

%S 3,5,53,173,293,2477,9173,22613,27653,61613,74093,92333,170957,360293,

%T 679733,847997,2004917,69009533,76553573,138473837,237536213,

%U 777133013,883597853,1728061733,2050312613,5534091197,9447241877,49107823133,65315700413

%N Increasing sequence of primes p such that all of 2,3,5,...,prime(n) are primitive roots mod p.

%C a(32) > 10^12. - _Dana Jacobsen_, Jul 13 2018

%H Dana Jacobsen, <a href="/A213052/b213052.txt">Table of n, a(n) for n = 1..31</a>

%o (PARI)

%o N=10^10;

%o default(primelimit,N);

%o A=2;

%o { forprime (p=3, N,

%o     q = 1;

%o     forprime (a=2, A,

%o         if ( znorder(Mod(a,p)) != p-1,  q=0; break() );

%o     );

%o     if ( q, A=nextprime(A+1); print1(p,", ") );

%o );}

%o (Perl)

%o use Math::Prime::Util ":all";

%o my($N,$A,$p,$a,@P7) = (10**11,2);

%o forprimes { $p=$_;

%o   if (   is_primitive_root(2,$p)

%o       && ($A < 3 || is_primitive_root(3,$p))

%o       && ($A < 5 || is_primitive_root(5,$p))

%o       && ($A < 7 || vecall { is_primitive_root($_,$p) } @P7)

%o     ) {

%o       print "$p\n";

%o       $A = next_prime($A);

%o       push @P7, $A if $A >= 7;

%o     }

%o } 3,$N;

%o # _Dana Jacobsen_, Jul 11 2018

%K nonn,hard

%O 1,1

%A _Joerg Arndt_, Jun 03 2012

%E a(20)-a(27) from _Joerg Arndt_, Apr 10 2016

%E a(28)-a(29) from _Dana Jacobsen_, Jul 11 2018