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A059647 Primes p such that x^63 = 2 has no solution mod p. 2
7, 13, 19, 29, 37, 43, 61, 67, 71, 73, 79, 97, 103, 109, 113, 127, 139, 151, 163, 181, 193, 197, 199, 211, 239, 241, 271, 281, 307, 313, 331, 337, 349, 367, 373, 379, 409, 421, 433, 449, 463, 487, 491, 523, 541, 547, 571, 577, 607, 613, 617, 619, 631, 659 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A049595 relative to A000040.

LINKS

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

MATHEMATICA

ok[p_] := Reduce[Mod[x^63 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2150]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

PROG

(MAGMA) [p: p in PrimesUpTo(700) | not exists{ x : x in ResidueClassRing(p) | x^63 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, 63), print1(p, ", ")));

/* Joerg Arndt, Sep 21 2012 */

CROSSREFS

Cf. A000040, A049595.

Sequence in context: A299928 A096452 A258038 * A059310 A299929 A287217

Adjacent sequences:  A059644 A059645 A059646 * A059648 A059649 A059650

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Feb 02 2001

STATUS

approved

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Last modified August 9 18:32 EDT 2020. Contains 336326 sequences. (Running on oeis4.)