A270800 Septic artiads: primes p congruent to 1 mod 14 for which all solutions of the congruence x^3 + x^2 - 2x - 1 == 0 (mod p) are 7th power residues.

14197, 21617, 23801, 24977, 25999, 34763, 37549, 41959, 42407, 45053, 45599, 54713, 55987, 56099, 60271, 61657, 63463, 66067, 72577, 75307, 76343, 76777, 79283, 83357, 88397, 90469, 91309, 99611, 107927, 111217, 111301, 111791, 124699, 126127, 131251, 132287

Offset

1,1

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

E. Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 1966 118-131. See page 126 (but beware errors).

E. Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 1966 118-131 [annotated and corrected scanned copy]

Prog

(Sage)
def is_septic_artiad(n) :
    if not (n % 14 == 1 and is_prime(n)) : return False
    R.<t> = PolynomialRing(GF(n))
    return all(r[0]^((n-1)//7) == 1 for r in (t^3 + t^2 - 2*t - 1).roots())
# Eric M. Schmidt, Apr 02 2016

Crossrefs

Cf. A001583.

Sequence in context: A258532 A258525 A254917 * A271247 A212949 A205202

Adjacent sequences: A270797 A270798 A270799 * A270801 A270802 A270803

Keyword

nonn

Author

N. J. A. Sloane, Apr 01 2016

Extensions

Definition added and sequence extended and corrected by Eric M. Schmidt, Apr 02 2016

Status

approved