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

1,1

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

Mathematica

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

Prog

(PARI)
forprime(p=2, 2000, if([]~!=polrootsmod(x^64+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */
(Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^64 eq - 2}]; // Vincenzo Librandi, Sep 16 2012

Crossrefs

Sequence in context: A051073 A051077 A051085 * A045339 A051091 A085902

Adjacent sequences: A051098 A051099 A051100 * A051102 A051103 A051104

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Joerg Arndt, Jul 27 2011

Status

approved