cp's OEIS Frontend

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.

Showing 1-4 of 4 results.

A070188 Primes p such that x^12 = 2 has a solution mod p, but x^(12^2) = 2 has no solution mod p.

Original entry on oeis.org

113, 281, 353, 593, 617, 919, 1049, 1097, 1193, 1217, 1423, 1481, 1553, 1601, 1753, 1777, 1889, 1999, 2129, 2143, 2273, 2281, 2287, 2393, 2689, 2791, 2833, 3089, 3137, 3761, 3833, 4001, 4049, 4153, 4177, 4217, 4289, 4457, 4481, 4519, 4657, 4663, 4817
Offset: 1

Views

Author

Klaus Brockhaus, Apr 29 2002

Keywords

Crossrefs

Cf. A049544, A059667, A070179 - A070187.

Programs

  • Magma
    [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^144 eq 2} and exists{x: x in ResidueClassRing(p) | x^12 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • PARI
    forprime(p=2,5000,x=0; while(x
  • PARI
    ok(p, r, k1, k2)={
    if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
    if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
    return(1);
}
forprime(p=2,10^5, if (ok(p,2,12,12^2),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */

A059264 Primes p such that x^12 = 2 has no solution mod p.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 283, 293, 307, 313, 317, 331, 337, 347, 349, 367, 373, 379, 389
Offset: 1

Views

Author

Klaus Brockhaus, Jan 23 2001

Keywords

Comments

Complement of A049544 relative to A000040.
Coincides for the first 119 terms with sequence of primes p such that x^36 = 2 has no solution mod p (first divergence is at 919, cf. A059668).

Links

Crossrefs

Cf. A000040, A049544, A049568, A059668.

Programs

  • Mathematica
    ok[p_] := Reduce[Mod[x^12 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]],ok] (* Vincenzo Librandi, Sep 14 2012 *)
Select[ Prime@ Range@ PrimePi@400, !MemberQ[ PowerMod[ Range@#, 12, #], Mod[2, #]] &] (* Robert G. Wilson v, Nov 05 2016 after Bruno Berselli in A059362 *)

A059668 Primes p such that x^36 = 2 has no solution mod p, but x^12 = 2 has a solution mod p.

Original entry on oeis.org

919, 1423, 1999, 2143, 2287, 2791, 4177, 4519, 4663, 5113, 5167, 6679, 6967, 8713, 9631, 9649, 9721, 11863, 12241, 12583, 12799, 13591, 16111, 17551, 18127, 20359, 20719, 21529, 21727, 21799, 22807, 23041, 23473, 23743, 23833, 23887, 23977
Offset: 1

Views

Author

Klaus Brockhaus, Feb 04 2001

Keywords

Links

Crossrefs

A000040, A049568, A049544, A059264.

Programs

  • Magma
    [p: p in PrimesUpTo(24000) | not exists{x: x in ResidueClassRing(p) | x^36 eq 2} and exists{x: x in ResidueClassRing(p) | x^12 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • Mathematica
    Select[Prime[Range[PrimePi[30000]]], ! MemberQ[PowerMod[Range[#], 36, #], Mod[2, #]]&& MemberQ[PowerMod[Range[#], 12, #], Mod[2, #]] &] (* Vincenzo Librandi, Sep 22 2013 *)

A059331 Primes p such that x^24 = 2 has no solution mod p, but x^12 = 2 has a solution mod p.

Original entry on oeis.org

113, 281, 353, 593, 617, 1049, 1097, 1193, 1481, 1601, 1753, 1889, 2129, 2273, 2281, 2393, 2689, 3089, 3137, 3761, 3833, 4001, 4153, 4217, 4289, 4457, 4657, 4817, 4937, 5113, 5393, 5569, 6521, 6569, 6761, 7481, 7577, 7793, 7817, 7841, 8273, 8369, 8537
Offset: 1

Views

Author

Klaus Brockhaus, Jan 26 2001

Keywords

Links

Crossrefs

A000040, A049556, A049544, A059264.

Programs

  • Magma
    [p: p in PrimesUpTo(9000) | not exists{x: x in ResidueClassRing(p) | x^24 eq 2} and exists{x: x in ResidueClassRing(p) | x^12 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • Mathematica
    Select[Prime[Range[PrimePi[1000]]], !MemberQ[PowerMod[Range[#], 24, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 12, #], Mod[2, #]]&] (* Vincenzo Librandi, Sep 21 2013 *)
Showing 1-4 of 4 results.

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