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A240583 Odd primes satisfying a specific condition (see comments). 2
47, 79, 167, 191, 223, 239, 263, 359, 367, 383, 431, 439, 463, 479, 503, 599, 607, 719, 823, 839, 863, 887, 911, 983, 1031, 1039, 1087, 1103, 1223, 1231, 1303, 1319, 1327, 1367, 1399, 1439, 1447, 1487, 1511, 1543, 1559, 1583, 1663, 1759, 1823, 1831, 1847 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Condition on odd prime p so that Q(Cp) is not rational over Q: p = 2q+1 where q = -1 (mod 4), q is squarefree, and any of 4p-q and q+1 is not square.

LINKS

Table of n, a(n) for n=1..47.

Shizuo Endo and Takehiko Miyata, Invariants of finite abelian groups, J. Math. Soc. Japan, Volume 25, Number 1 (1973), 1-167 (see Proposition 3.6 (i) p.18).

Akinari Hoshi, On Noether's problem for cyclic groups of prime order, arXiv:1402.3678 [math.NT], 2014 (see Proposition 3.1 (i) p.4 and Table 1 p.19).

MATHEMATICA

Select[Prime[Range[2, 300]], (q = (#-1)/2; SquareFreeQ[q] && Mod[q, 4] == 3 && !IntegerQ[Sqrt[4#-q]] && !IntegerQ[Sqrt[q+1]])&] (* Jean-Fran├žois Alcover, Sep 22 2018 *)

PROG

(PARI) isok(p) = isprime(p) && ((q = (p-1)/2) && issquarefree(q) && ((q % 4) == 3) && (!issquare(4*p-q)));

CROSSREFS

Cf. A240584, A240585.

Sequence in context: A132259 A046002 A132257 * A132255 A142041 A190799

Adjacent sequences:  A240580 A240581 A240582 * A240584 A240585 A240586

KEYWORD

nonn

AUTHOR

Michel Marcus, Apr 08 2014

STATUS

approved

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Last modified August 5 14:57 EDT 2021. Contains 346469 sequences. (Running on oeis4.)