A051101 Primes p such that x^64 = -2 has a solution mod p.

2, 3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251, 281, 283, 307, 331, 347, 379, 419, 443, 467, 491, 499, 523, 547, 563, 571, 587, 617, 619, 643, 659, 683, 691, 739, 787, 811, 827, 859, 883, 907, 947, 971, 1019, 1033, 1049, 1051, 1091, 1097, 1123, 1163, 1171, 1187

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Differs from A051085 first at the 541st entry, at p=15809. - R. J. Mathar, Oct 14 2008

From Christopher J. Smyth, Jul 24 2009: (Start)

Differs from A163183 (primes dividing 2^j+1 for some odd j) at the 827th entry, at p=25601. See comment at A163186 for explanation.

Sequence is union of A163183 and A163186 (primes p such that the equation x^64 = -2 mod p has a solution, and ord_p(-2) is even).

(End)

Complement of A216777 relative to A000040. - Vincenzo Librandi, Sep 17 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Programs

Magma

[p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^64 eq - 2}]; // Vincenzo Librandi, Sep 16 2012

Mathematica

ok[p_]:= Reduce[Mod[x^64 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[400]], ok] (* Vincenzo Librandi, Sep 16 2012 *)

PARI

forprime(p=2, 2000, if([]~!=polrootsmod(x^64+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */

Extensions

More terms from Joerg Arndt, Jul 27 2011