A240585 Odd primes satisfying a specific condition (see comments).

19, 23, 163, 487, 1459, 2663, 39367, 410759, 715823, 2450087, 12872687, 13935743, 23394167, 86093443, 160125983, 219804479, 236741543, 258280327, 2116179719, 3991233959, 4715895383, 6109873703, 8487319319, 9264815927, 12601744847

Offset

1,1

Comments

Condition on odd prime p so that Q(Cp^2) is not rational over Q.

Let p>7 is an odd prime which does not satisfy any of the following conditions:

(i) p = 2*3^s + 1, s >=0 where s !== -1 modulo 4.

(ii) p = 2*11^(2s+1) + 1, s>=0.

(iii) p = 2*q^(2s+1) + 1, s>=1 where q is an odd prime such that q == -1 modulo mod 12, q >= 23.

Links

Table of n, a(n) for n=1..25.

Shizuo Endo and Takehiko Miyata, Invariants of finite abelian groups, J. Math. Soc. Japan, Volume 25, Number 1 (1973), 1-167 (see Proposition 3.7 p.19).

Prog

(PARI) iscondi(p) = (r = (p-1)/2) && (k = ispower(r, , &n)) && (n == 3) && (k >= 2) && ((k % 4) != 3);
iscondii(p) = (r = (p-1)/2) && ((r == 11) || ((k = ispower(r, , &n)) && (n == 11) && (k % 2)));
iscondiii(p) = (r = (p-1)/2) && (k = ispower(r, , &n)) && isprime(n) && (n >= 23) && ((n % 12) == 11) && (k >= 3) && (k % 2);
isok(p) = isprime(p) && (iscondi(p) || iscondii(p) || iscondiii(p));

Crossrefs

Cf. A240583, A240584.

Sequence in context: A288614 A033214 A107185 * A226607 A284495 A160077

Adjacent sequences: A240582 A240583 A240584 * A240586 A240587 A240588

Keyword

nonn,more

Author

Michel Marcus, Apr 08 2014

Status

approved