A049580 -id:A049580 - cp's OEIS frontend

A212376 Primes p such that x^48 = 2 has no solution mod p.

3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 367

Offset: 1

Bruno Berselli, Sep 14 2012

Complement of A049580 relative to A000040.

This sequence is not the same as A059362. First disagreement at index 162: a(162)=1217, A059362(162)=1229.

Bruno Berselli, Table of n, a(n) for n = 1..1000

Cf. A000040, A049580.

Cf. A059362.

[p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^48 ne 2}];

Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 48, #], Mod[2, #]] &]
ok[p_] := Reduce[Mod[x^48 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[75]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

N=10^4;  default(primelimit,N);
ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
forprime(p=2,N, if (! ok(p,2,48),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */

A059669 Primes p such that x^48 = 2 has no solution mod p, but x^24 = 2 has a solution mod p.

Original entry on oeis.org

1217, 1553, 1777, 2833, 4049, 4481, 5297, 6449, 6689, 7121, 8081, 8609, 9137, 9281, 9649, 10337, 10433, 11329, 11633, 12241, 13121, 14321, 14753, 15569, 16433, 16673, 18257, 19793, 23057, 25169, 25889, 26177, 26561, 26993, 27281, 28001, 29153, 29201

Offset: 1

Klaus Brockhaus, Feb 04 2001

Vincenzo Librandi, Table of n, a(n) for n = 1..188

Cf. A000040, A049556, A059362, A049580.

[p: p in PrimesUpTo(30000) | not exists{x: x in ResidueClassRing(p) | x^48 eq 2} and exists{x: x in ResidueClassRing(p) | x^24 eq 2}]; // Vincenzo Librandi, Sep 21 2012

Select[Prime[Range[PrimePi[30000]]], ! MemberQ[PowerMod[Range[#], 48, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 24, #], Mod[2, #]] &] (* Vincenzo Librandi, Sep 22 2013 *)

a(37)-a(38) from Vincenzo Librandi, Sep 21 2012

cp's OEIS Frontend

A212376 Primes p such that x^48 = 2 has no solution mod p.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI