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

%I A049550 #23 Sep 05 2025 23:46:46
%S A049550 2,17,23,31,41,47,71,89,113,127,137,167,191,223,233,239,257,263,281,
%T A049550 311,353,359,383,401,431,439,449,457,479,503,521,569,593,599,601,617,
%U A049550 641,647,719,727,743,761,809,839,857,863,881,887,911,929,953,977,983
%N A049550 Primes p such that x^18 = 2 has a solution mod p.
%C A049550 Coincides with sequence of primes p such that x^54 = 2 has a solution mod p for the first 167 terms (and then diverges).
%H A049550 R. J. Mathar, <a href="/A049550/b049550.txt">Table of n, a(n) for n = 1..1000</a>
%H A049550 <a href="/index/Pri#smp">Index entries for related sequences</a>
%e A049550 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
%t A049550 ok[p_]:= Reduce[Mod[x^18- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 13 2012 *)
%o A049550 (PARI) forprime(p=2,2000,if([]~!=polrootsmod(x^18-2,p),print1(p,", ")));print(); /* _Joerg Arndt_, Jul 27 2011 */
%o A049550 (Magma) [p: p in PrimesUpTo(1000) | exists(t){x : x in ResidueClassRing(p) | x^18 eq 2}]; // _Vincenzo Librandi_, Sep 13 2012
%Y A049550 Cf. A000040.
%K A049550 nonn,easy,changed
%O A049550 1,1
%A A049550 _N. J. A. Sloane_