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A045316 Primes p such that x^8 = 2 has no solution mod p. 4
3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 83, 97, 101, 107, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 241, 251, 269, 277, 281, 283, 293, 307, 313, 317, 331, 347, 349, 353, 373, 379, 389 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A045315 relative to A000040. Coincides for the first 140 terms with the sequence of primes p such that x^16 = 2 has no solution mod p (first divergence is at 1217, cf. A059287) - Klaus Brockhaus, Jan 26 2001.

LINKS

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

MATHEMATICA

ok[p_]:= Reduce[Mod[x^8 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 19 2012  *)

PROG

(MAGMA) [p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^8 eq 2} ]; // Vincenzo Librandi, Sep 19 2012

CROSSREFS

Cf. A000040, A045315, A059287.

Sequence in context: A059641 A014662 A059349 * A040100 A076757 A178942

Adjacent sequences:  A045313 A045314 A045315 * A045317 A045318 A045319

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 20 09:12 EDT 2019. Contains 324234 sequences. (Running on oeis4.)