A059287 Primes p such that x^16 = 2 has no solution mod p, but x^8 = 2 has a solution mod p.

1217, 1249, 1553, 1777, 2833, 4049, 4273, 4481, 4993, 5297, 6449, 6481, 6689, 7121, 8081, 8609, 9137, 9281, 9649, 10337, 10369, 10433, 11329, 11617, 11633, 12241, 12577, 13121, 13441, 13633, 14321, 14753, 15121, 15569, 16417, 16433, 16673

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..150

Mathematica

Select[Prime[Range[PrimePi[20000]]], !MemberQ[PowerMod[Range[#], 16, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 8, #], Mod[2, #]]&] (* Vincenzo Librandi, Sep 21 2013 *)

Prog

(Magma) [p: p in PrimesUpTo(17000) | not exists{x: x in ResidueClassRing(p) | x^16 eq 2} and exists{x: x in ResidueClassRing(p) | x^8 eq 2}]; // Vincenzo Librandi, Sep 21 2012
(PARI) select( {is_A059287(p)=Mod(2, p)^(p\gcd(8, p-1))==1&&Mod(2, p)^(p\gcd(16, p-1))!=1}, primes(1999)) \\ Could any composite number pass this test? - M. F. Hasler, Jun 22 2024
(Python)
from itertools import islice
from sympy import is_nthpow_residue, nextprime
def A059287_gen(startvalue=2): # generator of terms >= startvalue
    p = max(1, startvalue-1)
    while (p:=nextprime(p)):
        if is_nthpow_residue(2, 8, p) and not is_nthpow_residue(2, 16, p):
            yield p
A059287_list = list(islice(A059287_gen(), 10)) # Chai Wah Wu, Jun 23 2024

Crossrefs

Cf. A000040, A045315, A045316.

Cf. A070184 (same with x^64 instead of x^16).

Sequence in context: A331625 A235889 A321062 * A225759 A059669 A032628

Adjacent sequences: A059284 A059285 A059286 * A059288 A059289 A059290

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 25 2001

Status

approved