A239901 - OEIS

%I #11 Oct 01 2014 10:17:49

%S 13,17,41,53,101,137,149,277,313,317,389,401,433,449,521,557,569,673,

%T 677,701,761,769,809,857,877,953,977,1009,1129,1213,1277,1297,1361,

%U 1373,1409,1489,1493,1549,1613,1637,1657,1697,1709,1741,1789,1861,1873,1901

%N Primes p such that ((p-1)/4)! is a primitive root mod p.

%D John B. Cosgrave and Karl Dilcher, The multiplicative orders of certain Gauss factorials, II, Preprint, 2014.

%H Hiroaki Yamanouchi, <a href="/A239901/b239901.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI)

%o isok(n) = {

%o   ret = 1;

%o   if(n % 4 == 1 && isprime(n),

%o     m = (n - 1) / 4;

%o     r = m! % n;

%o     f = factor(n - 1);

%o     l = length(f~);

%o     for(i=1, l,

%o       if(Mod(r^((n-1)/f[i, 1]), n) == 1,

%o         ret = 0;

%o       );

%o     );

%o   ,

%o     ret = 0;

%o   );

%o   ret;

%o } \\ _Hiroaki Yamanouchi_, Sep 30 2014

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Apr 06 2014

%E a(11)-a(48) from _Hiroaki Yamanouchi_, Sep 30 2014