%I #31 Feb 21 2022 01:04:56

%S 2,7,23,31,47,71,73,79,89,103,127,151,167,191,199,223,233,239,257,263,

%T 271,311,337,359,367,383,431,439,463,479,487,503,599,601,607,631,647,

%U 719,727,743,751,823,839,863,881,887,911,919,937,967,983,991,1031,1039

%N Primes p such that x^8 = 2 has a solution mod p.

%C Coincides with the sequence of "primes p such that x^16 = 2 has a solution mod p" for first 58 terms (and then diverges).

%C Complement of A045316 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012

%D A. Aigner, Kriterien zum 8. und 16. Potenzcharakter der Reste 2 und -2, Deutsche Math. 4 (1939), 44-52; FdM 65 - I (1939), 112.

%H T. D. Noe, <a href="/A045315/b045315.txt">Table of n, a(n) for n = 1..1000</a>

%H H. Hasse, <a href="https://doi.org/10.1007/BF02854527">Der 2^n-te Potenzcharakter von 2 im Koerper der 2^n-ten Einheitswurzeln</a>, Rend. Circ. Matem. Palermo (2), 7 (1958), 185-243.

%H Franz Lemmermeyer, <a href="http://www.rzuser.uni-heidelberg.de/~hb3/recbib.html">Bibliography on Reciprocity Laws</a>

%H A. L. Whiteman, <a href="http://dx.doi.org/10.4153/CJM-1954-035-8">The sixteenth power residue character of 2</a>, Canad. J. Math. 6 (1954), 364-373; Zbl 55.27102.

%H <a href="/index/Pri#smp">Index entries for related sequences</a>

%t ok[p_] := Reduce[ Mod[x^8-2, p] == 0, x, Integers] =!= False; Select[ Prime[ Range[200] ], ok] (* _Jean-François Alcover_, Nov 28 2011 *)

%o (Magma) [p: p in PrimesUpTo(1100) | exists(t){x : x in ResidueClassRing(p) | x^8 eq 2}]; // _Vincenzo Librandi_, Sep 13 2012

%o (PARI) is(n)=isprime(n) && ispower(Mod(2,n),8) \\ _Charles R Greathouse IV_, Feb 08 2017

%Y Cf. A000040, A001132, A040028, A040098, A045316.

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_