A239901 Primes p such that ((p-1)/4)! is a primitive root mod p.

13, 17, 41, 53, 101, 137, 149, 277, 313, 317, 389, 401, 433, 449, 521, 557, 569, 673, 677, 701, 761, 769, 809, 857, 877, 953, 977, 1009, 1129, 1213, 1277, 1297, 1361, 1373, 1409, 1489, 1493, 1549, 1613, 1637, 1657, 1697, 1709, 1741, 1789, 1861, 1873, 1901

Offset

1,1

References

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

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..10000

Prog

(PARI)
isok(n) = {
  ret = 1;
  if(n % 4 == 1 && isprime(n),
    m = (n - 1) / 4;
    r = m! % n;
    f = factor(n - 1);
    l = length(f~);
    for(i=1, l,
      if(Mod(r^((n-1)/f[i, 1]), n) == 1,
        ret = 0;
      );
    );
  ,
    ret = 0;
  );
  ret;
} \\ Hiroaki Yamanouchi, Sep 30 2014

Crossrefs

Sequence in context: A043113 A043893 A279392 * A068497 A125524 A156553

Adjacent sequences: A239898 A239899 A239900 * A239902 A239903 A239904

Keyword

nonn

Author

N. J. A. Sloane, Apr 06 2014

Extensions

a(11)-a(48) from Hiroaki Yamanouchi, Sep 30 2014

Status

approved