A059349 - OEIS

%I #19 Jun 22 2024 02:28:47

%S 3,5,11,13,17,19,29,37,41,43,53,59,61,67,83,97,101,107,109,113,131,

%T 137,139,149,157,163,173,179,181,193,197,211,227,229,241,251,257,269,

%U 277,281,283,293,307,313,317,331,347,349,353,373,379,389,397,401,409,419

%N Primes p such that x^32 = 2 has no solution mod p.

%C Complement of A049564 relative to A000040.

%C Differs from A014662 first at p=6529, then at p=21569. [_R. J. Mathar_, Oct 05 2008]

%C Differs from A045316 (x^8 == 2 (mod p) has no solution) first at a(37) = 257 which is not a term of A045316. See A070184 for all such terms. - _M. F. Hasler_, Jun 21 2024

%H Vincenzo Librandi, <a href="/A059349/b059349.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^32 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok ] (* _Vincenzo Librandi_, Sep 20 2012  *)

%o (Magma) [p: p in PrimesUpTo(450) | not exists{x : x in ResidueClassRing(p) | x^32 eq 2 }]; // _Vincenzo Librandi_, Sep 20 2012

%Y Cf. A000040, A049564, A216747.

%Y Cf. A070184 = (this sequence) \ A045316.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jan 27 2001