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A059642 Primes p such that x^55 = 2 has no solution mod p. 2
11, 23, 31, 41, 61, 67, 71, 89, 101, 131, 181, 191, 199, 211, 271, 281, 311, 331, 353, 397, 401, 419, 421, 461, 463, 491, 521, 541, 601, 617, 631, 661, 683, 691, 701, 727, 751, 761, 811, 821, 859, 881, 941, 947, 991, 1021, 1031, 1051, 1061, 1091, 1123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A049587 relative to A000040.

LINKS

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

MATHEMATICA

ok[p_] := Reduce[Mod[x^55 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

PROG

(MAGMA) [p: p in PrimesUpTo(1150) | not exists{x: x in ResidueClassRing(p) | x^55 eq 2}]; // Vincenzo Librandi, Sep 21 2012

(PARI)

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, 55), print1(p, ", ")));

/* Joerg Arndt, Sep 21 2012 */

CROSSREFS

Cf. A000040, A049587.

Sequence in context: A337845 A030675 A110786 * A090920 A344175 A126330

Adjacent sequences:  A059639 A059640 A059641 * A059643 A059644 A059645

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Feb 02 2001

STATUS

approved

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)