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 A240584 Odd primes satisfying a specific condition (see comments). 2
 113, 137, 233, 521, 593, 617, 809, 977, 1033, 1097, 1129, 1193, 1289, 1361, 1489, 1553, 1609, 1777, 1993, 2129, 2153, 2281, 2417, 2441, 2473, 2609, 2729, 2833, 2897, 3049, 3089, 3121, 3209, 3217, 3433, 3593, 3761, 3793, 3881, 4073, 4241, 4273, 4297, 4337 (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 = 8q+1 where q != -1 (mod 4), q is squarefree, and any of p-q and p-4q is not square. LINKS Shizuo Endo and Takehiko Miyata, Invariants of finite abelian groups, J. Math. Soc. Japan, Volume 25, Number 1 (1973), 1-167 (see Proposition 3.6 (ii) p.18). Akinari Hoshi, On Noether's problem for cyclic groups of prime order, arXiv:1402.3678 [math.NT], 2014 (see Proposition 3.1 (ii) p.4 and Table 2 p.19). MATHEMATICA Reap[For[p = 3, p < 5000, p = NextPrime[p], If[Mod[p, 8] == 1 && Mod[q = Quotient[p, 8], 4] != 3 && SquareFreeQ[q] && AllTrue[{p-q, p-4q}, !IntegerQ[Sqrt[#]]&], Sow[p]]]][[2, 1]] (* Jean-François Alcover, Dec 15 2018 *) PROG (PARI) isok(p) = isprime(p) &&  ((type(q = (p-1)/8)== "t_INT") && ((q % 4) != 3) && (!issquare(p-q)) && (!issquare(p-4*q))); CROSSREFS Cf. A240583, A240585. Sequence in context: A224554 A095617 A139645 * A139988 A140005 A198319 Adjacent sequences:  A240581 A240582 A240583 * A240585 A240586 A240587 KEYWORD nonn AUTHOR Michel Marcus, Apr 08 2014 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)