login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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