A216743 -id:A216743 - cp's OEIS frontend

A051081 Primes p such that x^24 = -2 has a solution mod p.

2, 3, 11, 43, 59, 83, 107, 131, 179, 227, 251, 257, 281, 283, 307, 347, 419, 443, 467, 491, 499, 563, 587, 617, 643, 659, 683, 691, 739, 811, 827, 881, 947, 971, 1019, 1049, 1051, 1091, 1097, 1163, 1187, 1193, 1217, 1259, 1283, 1307, 1427, 1451, 1459, 1481

Offset: 1

N. J. A. Sloane

Complement of A216743 relative to A000040. - Vincenzo Librandi, Sep 17 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

[p: p in PrimesUpTo(1500) | exists(t){x : x in ResidueClassRing(p) | x^24 eq - 2}]; // Vincenzo Librandi, Sep 15 2012

isA051081 := proc(p) local x; for x from 0 to p-1 do if (x^24 mod p) = (-2 mod p) then RETURN(true) ; fi; od: RETURN(false) ; end: for i from 1 to 300 do p := ithprime(i) ; if isA051081(p) then printf("%d,",p) ; fi; od: # R. J. Mathar, Oct 15 2008

ok[p_]:= Reduce[Mod[x^24 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

PARI
```
/* see A051071 */
```

More terms from R. J. Mathar, Oct 15 2008

A216769 Primes p such that x^48 = -2 has no solution mod p.

Original entry on oeis.org

5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 61, 67, 71, 73, 79, 89, 97, 101, 103, 109, 113, 127, 137, 139, 149, 151, 157, 163, 167, 173, 181, 191, 193, 197, 199, 211, 223, 229, 233, 239, 241, 263, 269, 271, 277, 293, 311, 313, 317, 331, 337, 349, 353, 359

Offset: 1

Vincenzo Librandi, Sep 16 2012

Complement of A051093 relative to A000040.

Starts to differ from A216743 at index n=121 (presence/absence of 881). - R. J. Mathar, Jul 20 2023

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A051093, A216743.

[p: p in PrimesUpTo(600) | not exists{x: x in ResidueClassRing(p) | x^48 eq -2}];

ok[p_] := Reduce[Mod[x^48 + 2, p] == 0, x, Integers] == False;Select[Prime[Range[200]], ok]

cp's OEIS Frontend

A051081 Primes p such that x^24 = -2 has a solution mod p.

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