A271264 Septic artiads (A270800) congruent to 1 mod 98 and for which 7 is a 7th power residue.

876611, 1163653, 1471079, 1608769, 2367289, 2368759, 2538103, 2564857, 2621501, 2693629, 2774381, 3120713, 3495269, 3498797, 3636781, 3974881, 4240853, 4376681, 4571309, 4654217, 4702433, 4867171, 5047883, 5066993, 5629121, 5644213, 5760343, 5779649, 6262397

Offset: 1

Author

Eric M. Schmidt, Apr 03 2016

Keywords

• nonn

Comments

Septic hyperartiads (A270801) congruent to 1 mod 98.

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..100
• E. Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 1966 118-131. See p. 128-129, Theorem 8.
• E. Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 1966 118-131 [annotated and corrected scanned copy]

Crossrefs

Cf. A001583, A270800, A270801.

Programs

Sage

def isa(n) :
    if not (n % 98 == 1 and is_prime(n)) : return False
    R. = PolynomialRing(GF(n))
    return 7.powermod((n-1)//7, n) == 1 and all(r[0]^((n-1)//7) == 1 for r in (t^3 + t^2 - 2*t - 1).roots())