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Septic artiads (A270800) congruent to 1 mod 98 and for which 2 is a 7th power residue.
1

%I #12 Mar 07 2020 05:40:45

%S 874651,941879,1074277,1080451,1396697,2024387,2546237,2807603,

%T 3267419,3324847,3436273,3465673,3851009,4150301,4219979,4367567,

%U 4651963,4762507,5173813,5308759,5398919,5474477,5552191,5710363,6248579,6391267,6575507,6627251,6791107

%N Septic artiads (A270800) congruent to 1 mod 98 and for which 2 is a 7th power residue.

%H Eric M. Schmidt, <a href="/A271263/b271263.txt">Table of n, a(n) for n = 1..100</a>

%H E. Lehmer, <a href="http://dx.doi.org/10.1016/0022-247X(66)90145-4">Artiads characterized</a>, J. Math. Anal. Appl. 15 1966 118-131. See p. 128, Theorem 7.

%H E. Lehmer, <a href="/A001583/a001583b.pdf">Artiads characterized</a>, J. Math. Anal. Appl. 15 1966 118-131 [annotated and corrected scanned copy]

%o (Sage)

%o def isa(n) :

%o if not (n % 98 == 1 and is_prime(n)) : return False

%o R.<t> = PolynomialRing(GF(n))

%o return 2.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())

%Y Cf. A001583, A270800.

%K nonn

%O 1,1

%A _Eric M. Schmidt_, Apr 03 2016