A240584 Odd primes satisfying a specific condition (see comments).

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

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

Table of n, a(n) for n=1..44.

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