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 A240585 Odd primes satisfying a specific condition (see comments). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified July 26 10:18 EDT 2021. Contains 346294 sequences. (Running on oeis4.)