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A059223 Primes p such that x^37 = 2 has no solution mod p. 4
149, 223, 593, 1259, 1481, 1777, 1999, 2221, 2591, 2887, 3109, 3257, 3331, 3701, 3923, 4219, 4441, 4663, 5107, 5477, 6143, 6217, 6661, 6883, 7253, 7549, 7919, 7993, 8363, 8807, 9029, 9103, 9473, 9547, 9769, 10139, 10657, 11027, 12211, 12433 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A049569 relative to A000040.

Presumably this is also Primes congruent to 1 mod 37 (A216970). - N. J. A. Sloane, Jul 11 2008

Not so. The smallest counterexample is 11471: 11471 == 1 (mod 37), but 43^37 == 2 (mod 11471), therefore this prime is not in the sequence. - Bruno Berselli, Sep 12 2012

LINKS

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

MATHEMATICA

Select[Prime[Range[PrimePi[12500]]], ! MemberQ[PowerMod[Range[#], 37, #], Mod[2, #]] &] (* T. D. Noe, Sep 12 2012 *)

ok[p_]:= Reduce[Mod[x^37 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2000]], ok] (* Vincenzo Librandi, Sep 19 2012  *)

PROG

(MAGMA) [p: p in PrimesUpTo(13000) | forall{x: x in ResidueClassRing(p) | x^37 ne 2}]; // Bruno Berselli, Sep 12 2012

(PARI)

N=10^5;  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, 37), print1(p, ", ")));

/* Joerg Arndt, Sep 21 2012 */

CROSSREFS

Cf. A000040, A049569, A216970.

Sequence in context: A128390 A142029 A216970 * A096694 A144315 A267490

Adjacent sequences:  A059220 A059221 A059222 * A059224 A059225 A059226

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jan 19 2001

STATUS

approved

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)