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 1-5 of 5 results.

A040993 Primes p such that x^6 = 2 has no solution mod p.

Original entry on oeis.org

3, 5, 7, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 131, 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, 397, 409
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Complement of A040992 relative to A000040. Coincides for the first 58 terms with A212375, that is the sequence of primes p such that x^18 = 2 has no solution mod p (first divergence is at 433, cf. A059664). Also coincides for the first 58 terms with sequence of primes p such that x^54 = 2 has no solution mod p (first divergence is at 433, cf. A059665). The sequence for x^18 and the sequence for x^54 coincide for the first 379 terms (first divergence is at 3943, cf. A059666). - Klaus Brockhaus, Feb 04 2001

Links

Crossrefs

Cf. A000040, A040992, A049550, A059664, A059665, A059666, A212375.

Programs

  • Magma
    [p: p in PrimesUpTo(500) | forall{x: x in ResidueClassRing(p) | x^6 ne 2}]; // Bruno Berselli, Sep 13 2012
  • Mathematica
    Select[Prime[Range[PrimePi[500]]], ! MemberQ[PowerMod[Range[#], 6, #], Mod[2, #]] &] (* Bruno Berselli, Sep 13 2012 *)
ok[p_] := Reduce[Mod[x^6 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Extensions

A212375 added in the Brockhaus comment from Bruno Berselli, Sep 13 2012

A059664 Primes p such that x^18 = 2 has no solution mod p, but x^6 = 2 has a solution mod p.

Original entry on oeis.org

433, 919, 1423, 1999, 2017, 2143, 2287, 2791, 2953, 3457, 3889, 4177, 4519, 4663, 5113, 5167, 6679, 6967, 8713, 9631, 9649, 9721, 10009, 11863, 12241, 12583, 12799, 13177, 13591, 15913, 16057, 16111, 16561, 16921, 17551, 18127, 18793, 19081
Offset: 1

Views

Author

Klaus Brockhaus, Feb 04 2001

Keywords

Links

Crossrefs

A000040, A040992, A040993, A049550, A059665.

Programs

  • Magma
    [p: p in PrimesUpTo(20000) | not exists{x: x in ResidueClassRing(p) | x^18 eq 2} and exists{x: x in ResidueClassRing(p) | x^6 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • Mathematica
    Select[Prime[Range[PrimePi[20000]]], !MemberQ[PowerMod[Range[#], 18, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 6, #], Mod[2, #]]&] (* Vincenzo Librandi, Sep 21 2013 *)

A059665 Primes p such that x^54 = 2 has no solution mod p, but x^6 = 2 has a solution mod p.

Original entry on oeis.org

433, 919, 1423, 1999, 2017, 2143, 2287, 2791, 2953, 3457, 3889, 3943, 4177, 4519, 4663, 5113, 5167, 6679, 6967, 8713, 9631, 9649, 9721, 10009, 11287, 11863, 12241, 12583, 12799, 13177, 13591, 15913, 16057, 16111, 16561, 16921, 17551, 18127
Offset: 1

Views

Author

Klaus Brockhaus, Feb 04 2001

Keywords

Links

Crossrefs

A000040, A040992, A040993, A049550, A059666, A059664.

Programs

  • Magma
    [p: p in PrimesUpTo(20000) | not exists{x: x in ResidueClassRing(p) | x^54 eq 2} and exists{x: x in ResidueClassRing(p) | x^6 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • Mathematica
    Select[Prime[Range[PrimePi[20000]]], !MemberQ[PowerMod[Range[#], 54, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 6, #], Mod[2, #]] &] (* Vincenzo Librandi, Sep 21 2013 *)

A059666 Primes p such that x^54 = 2 has no solution mod p, but x^18 = 2 has a solution mod p.

Original entry on oeis.org

3943, 11287, 20143, 23599, 25759, 26407, 29863, 32833, 33751, 38287, 39367, 39799, 46441, 47737, 47791, 59887, 62047, 63127, 68311, 73063, 79273, 82351, 84457, 84673, 88129, 90289, 91639, 93529, 94447, 101089, 104761, 107839, 140617, 144073, 146449, 150607
Offset: 1

Views

Author

Klaus Brockhaus, Feb 05 2001

Keywords

Links

Crossrefs

A000040, A049550, A040993.

Programs

  • Magma
    [p: p in PrimesUpTo(40000) | not exists{x: x in ResidueClassRing(p) | x^54 eq 2} and exists{x: x in ResidueClassRing(p) | x^18 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • Mathematica
    Select[Prime[Range[PrimePi[200000]]],!MemberQ[PowerMod[Range[#],54,#],Mod[2,#]] && MemberQ[PowerMod[Range[#],18,#],Mod[2,#]]&] (* Vincenzo Librandi, Sep 21 2013 *)

Extensions

More terms from Vincenzo Librandi, Sep 21 2013

A212375 Primes p such that x^18 = 2 has no solution mod p.

Original entry on oeis.org

3, 5, 7, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 131, 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, 397
Offset: 1

Views

Author

Bruno Berselli, Sep 13 2012

Keywords

Comments

Complement of A049550 relative to A000040.
This sequence is not the same as A040993. First disagreement at index 59: a(59)=433, A040993(59)=443.

Links

Crossrefs

Cf. A000040, A049550.
Cf. A040993.

Programs

  • Magma
    [p: p in PrimesUpTo(500) | forall{x: x in ResidueClassRing(p) | x^18 ne 2}];
  • Magma
    [p: p in PrimesUpTo(400) | not exists{x : x in ResidueClassRing(p) | x^18 eq 2} ]; // Vincenzo Librandi, Sep 20 2012
  • Mathematica
    Select[Prime[Range[PrimePi[500]]], ! MemberQ[PowerMod[Range[#], 18, #], Mod[2, #]] &]
ok[p_]:= Reduce[Mod[x^18 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* Vincenzo Librandi, Sep 20 2012  *)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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