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A040036 Primes p such that x^3 = 3 has a solution mod p. 2
2, 3, 5, 11, 17, 23, 29, 41, 47, 53, 59, 61, 67, 71, 73, 83, 89, 101, 103, 107, 113, 131, 137, 149, 151, 167, 173, 179, 191, 193, 197, 227, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 317, 347, 353, 359, 367, 383, 389, 401, 419, 431, 439, 443, 449, 461, 467, 479, 491, 499 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A040038 relative to A000040. - Vincenzo Librandi, Sep 13 2012

Being a cube mod p is a necessary condition for 3 to be a 9th power mod p. See Williams link pp. 1, 8 (warning: term 271 is missed). - Michel Marcus, Nov 12 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Kenneth S. Williams, 3 as a Ninth Power (mod p), Math. Scand. Vol 35 (1974), 309-317.

MAPLE

select(p -> isprime(p) and numtheory:-mroot(3, 3, p) <> FAIL, [2, seq(i, i=3..1000, 2)]); # Robert Israel, Nov 12 2017

MATHEMATICA

ok [p_]:=Reduce[Mod[x^3 - 3, p] == 0, x, Integers] =!= False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 11 2012 *)

PROG

(MAGMA) [p: p in PrimesUpTo(450) | exists(t){x : x in ResidueClassRing(p) | x^3 eq 3}]; // Vincenzo Librandi, Sep 11 2012

(PARI) isok(p) = isprime(p) && ispower(Mod(3, p), 3); \\ Michel Marcus, Nov 12 2017

CROSSREFS

Cf. A000040, A040038. Contains A003627.

Sequence in context: A098058 A040054 A093503 * A040078 A045309 A103664

Adjacent sequences:  A040033 A040034 A040035 * A040037 A040038 A040039

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 13 02:09 EDT 2020. Contains 336441 sequences. (Running on oeis4.)