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A049573 Primes p such that x^41 = 2 has a solution mod p.

%I A049573 #24 Jul 20 2025 07:25:11
%S A049573 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,89,97,
%T A049573 101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,
%U A049573 191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277
%N A049573 Primes p such that x^41 = 2 has a solution mod p.
%C A049573 Differs from A000040: 83 does not occur.
%H A049573 R. J. Mathar, <a href="/A049573/b049573.txt">Table of n, a(n) for n = 1..1000</a>
%H A049573 <a href="/index/Pri#smp">Index entries for related sequences</a>
%e A049573 0^41 == 2 (mod 2). 2^41 == 2 (mod 3). 2^41 == 2 (mod 5). 4^41 == 2 (mod 7). 2^41 == 2 (mod 11). 6^41 == 2 (mod 13). 2^41 == 2 (mod 17). 15^41 == 2 (mod 19). 13^41 == 2 (mod 23). 14^41 == 2 (mod 29). 2^41 == 2 (mod 31). 24^41 == 2 (mod 37). 2^41 == 2 (mod 41). 22^41 == 2 (mod 43). - _R. J. Mathar_, Jul 20 2025
%t A049573 ok[p_]:= Reduce[Mod[x^41 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 14 2012 *)
%o A049573 (Magma) [p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^41 eq 2}]; // _Vincenzo Librandi_, Sep 14 2012
%Y A049573 Cf. A000040, A059236 for primes not in this sequence.
%K A049573 nonn,easy
%O A049573 1,1
%A A049573 _N. J. A. Sloane_