A049556 -id:A049556 - cp's OEIS frontend

A059362 Primes p such that x^24 = 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

Klaus Brockhaus, Jan 27 2001

Complement of A049556 relative to A000040.
Coincides for the first 23 terms with sequence A059264 of primes p such that x^12 = 2 has no solution mod p (first divergence is at 113, cf. A059331).
Coincides for the first 161 terms with sequence A212376 of primes p such that x^48 = 2 has no solution mod p (first divergence is at 1217, cf. A059669).

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

Cf. A000040, A049556, A059264, A059331, A059669, A212376.

[p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^24 ne 2}]; // Bruno Berselli, Sep 14 2012

Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 24, #], Mod[2, #]] &] (* Bruno Berselli, Sep 14 2012 *)
ok[p_] := Reduce[Mod[x^24 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* Vincenzo Librandi, Sep 20 2012 *)

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

Klaus Brockhaus, Jan 26 2001

Vincenzo Librandi, Table of n, a(n) for n = 1..370

A000040, A049556, A049544, A059264.

[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

Select[Prime[Range[PrimePi[1000]]], !MemberQ[PowerMod[Range[#], 24, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 12, #], Mod[2, #]]&] (* Vincenzo Librandi, Sep 21 2013 *)

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

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A059362 Primes p such that x^24 = 2 has no solution mod p.

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

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

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