A040047 Primes p such that x^3 = 6 has no solution mod p.

13, 19, 31, 43, 61, 67, 73, 79, 97, 103, 109, 127, 151, 157, 193, 199, 211, 223, 229, 271, 277, 283, 331, 367, 373, 397, 433, 457, 463, 487, 523, 547, 577, 601, 613, 619, 661, 673, 691, 709, 733, 739, 757, 769

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A040046 relative to A000040. - Vincenzo Librandi, Sep 17 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Benjamin Braun, Brian Davis, Antichain Simplices, arXiv:1901.01417 [math.CO], 2019.
• Stepan Kochemazov, Oleg Zaikin, Eduard Vatutin, Alexey Belyshev, Enumerating Diagonal Latin Squares of Order Up to 9, J. Int. Seq., Vol. 23 (2020), Article 20.1.2.

Programs

Magma

[p: p in PrimesUpTo(1000) | not exists{x : x in ResidueClassRing(p) | x^3 eq 6} ]; // Vincenzo Librandi, Sep 17 2012

Mathematica

ok[p_]:= Reduce[Mod[x^3 - 6, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 17 2012 *)