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

1,1

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).

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Index entries for related sequences

Example

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

Mathematica

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

Prog

(PARI) forprime(p=2, 2000, if([]~!=polrootsmod(x^18-2, p), print1(p, ", "))); print(); /* Joerg Arndt, Jul 27 2011 */
(Magma) [p: p in PrimesUpTo(1000) | exists(t){x : x in ResidueClassRing(p) | x^18 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040.

Sequence in context: A126961 A106622 A040992 * A049574 A018643 A094668

Adjacent sequences: A049547 A049548 A049549 * A049551 A049552 A049553

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved