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%I #17 Sep 08 2022 08:44:58
%S 2,17,23,31,41,47,71,89,113,127,137,167,191,223,233,239,257,263,281,
%T 311,353,359,383,401,431,439,449,457,479,503,521,569,593,599,601,617,
%U 641,647,719,727,743,761,809,839,857,863,881,887,911,929,953,977,983
%N Primes p such that x^18 = 2 has a solution mod p.
%C 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 R. J. Mathar, <a href="/A049550/b049550.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Pri#smp">Index entries for related sequences</a>
%t ok[p_]:= Reduce[Mod[x^18- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 13 2012 *)
%o (PARI) forprime(p=2,2000,if([]~!=polrootsmod(x^18-2,p),print1(p,", ")));print();
%o /* Joerg Arndt, Jul 27 2011 */
%o (Magma) [p: p in PrimesUpTo(1000) | exists(t){x : x in ResidueClassRing(p) | x^18 eq 2}]; // _Vincenzo Librandi_, Sep 13 2012
%Y Cf. A000040.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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