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
Differs from A059349 (x^32 == 2 (mod p) has no solution) first at a(37) = A059349(38), the term A059349(37) = 257 which is not in this sequence. See A070184 for all such terms. - M. F. Hasler, Jun 21 2024
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
(PARI) select( {is_A045316(p)=Mod(2, p)^(p\gcd(8, p-1))!=1 && p>2}, primes(199)) \\ Append "&& isprime(p)" if that's not known. - M. F. Hasler, Jun 22 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved