A049550 Primes p such that x^18 = 2 has a solution mod p.

2, 17, 23, 31, 41, 47, 71, 89, 113, 127, 137, 167, 191, 223, 233, 239, 257, 263, 281, 311, 353, 359, 383, 401, 431, 439, 449, 457, 479, 503, 521, 569, 593, 599, 601, 617, 641, 647, 719, 727, 743, 761, 809, 839, 857, 863, 881, 887, 911, 929, 953, 977, 983

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Coincides with sequence of primes p such that x^54 = 2 has a solution mod p for the first 167 terms (and then diverges).

Examples

			0^18 == 2 (mod 2). 6^18 == 2 (mod 17). 3^18 == 2 (mod 23). 4^18 == 2 (mod 31). 15^18 == 2 (mod 41). 5^18 == 2 (mod 47). 4^18 == 2 (mod 71). 11^18 == 2 (mod 89). - _R. J. Mathar_, Jul 20 2025
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• Index entries for related sequences

Crossrefs

Cf. A000040.

Programs

Magma

[p: p in PrimesUpTo(1000) | exists(t){x : x in ResidueClassRing(p) | x^18 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Mathematica

ok[p_]:= Reduce[Mod[x^18- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

PARI

forprime(p=2,2000,if([]~!=polrootsmod(x^18-2,p),print1(p,", ")));print();
/* Joerg Arndt, Jul 27 2011 */