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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.

%I A270800 #16 Mar 06 2020 15:47:03
%S A270800 14197,21617,23801,24977,25999,34763,37549,41959,42407,45053,45599,
%T A270800 54713,55987,56099,60271,61657,63463,66067,72577,75307,76343,76777,
%U A270800 79283,83357,88397,90469,91309,99611,107927,111217,111301,111791,124699,126127,131251,132287
%N 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.
%H A270800 Eric M. Schmidt, <a href="/A270800/b270800.txt">Table of n, a(n) for n = 1..1000</a>
%H A270800 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 page 126 (but beware errors).
%H A270800 E. Lehmer, <a href="/A001583/a001583b.pdf">Artiads characterized</a>, J. Math. Anal. Appl. 15 1966 118-131 [annotated and corrected scanned copy]
%o A270800 (Sage)
%o A270800 def is_septic_artiad(n) :
%o A270800     if not (n % 14 == 1 and is_prime(n)) : return False
%o A270800     R.<t> = PolynomialRing(GF(n))
%o A270800     return all(r[0]^((n-1)//7) == 1 for r in (t^3 + t^2 - 2*t - 1).roots())
%o A270800 # _Eric M. Schmidt_, Apr 02 2016
%Y A270800 Cf. A001583.
%K A270800 nonn
%O A270800 1,1
%A A270800 _N. J. A. Sloane_, Apr 01 2016
%E A270800 Definition added and sequence extended and corrected by _Eric M. Schmidt_, Apr 02 2016