This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049580 #19 Jul 20 2025 07:25:58
%S A049580 2,23,31,47,71,89,127,167,191,223,233,239,257,263,311,359,383,431,439,
%T A049580 479,503,599,601,647,719,727,743,839,863,881,887,911,919,983,1031,
%U A049580 1103,1151,1223,1289,1319,1327,1367,1399,1423,1433,1439,1471,1487,1511,1559
%N A049580 Primes p such that x^48 = 2 has a solution mod p.
%C A049580 Complement of A212376 relative to A000040. - _Vincenzo Librandi_, Sep 14 2012
%H A049580 R. J. Mathar, <a href="/A049580/b049580.txt">Table of n, a(n) for n = 1..1000</a>
%H A049580 <a href="/index/Pri#smp">Index entries for related sequences</a>
%e A049580 0^48 == 2 (mod 2). 8^48 == 2 (mod 23). 4^48 == 2 (mod 31). 7^48 == 2 (mod 47). 33^48 == 2 (mod 71). 5^48 == 2 (mod 89). 10^48 == 2 (mod 127). 49^48 == 2 (mod 167). 4^48 == 2 (mod 191). - _R. J. Mathar_, Jul 20 2025
%t A049580 ok[p_]:= Reduce[Mod[x^48 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* _Vincenzo Librandi_, Sep 14 2012 *)
%o A049580 (Magma) [p: p in PrimesUpTo(1600) | exists(t){x : x in ResidueClassRing(p) | x^48 eq 2}]; // _Vincenzo Librandi_, Sep 14 2012
%o A049580 (PARI)
%o A049580 N=10^4; default(primelimit,N);
%o A049580 ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
%o A049580 forprime(p=2,N, if (ok(p,2,48),print1(p,", ")));
%o A049580 /* _Joerg Arndt_, Sep 21 2012 */
%Y A049580 Cf. A000040, A212376.
%K A049580 nonn,easy
%O A049580 1,1
%A A049580 _N. J. A. Sloane_