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Number of primes p < 10^n for which 2 is a cubic residue (mod p).
2

%I #18 May 23 2022 22:33:04

%S 3,16,112,818,6367,52299,442972,3840740,33898001,303369367,2745366812,

%T 25071938615

%N Number of primes p < 10^n for which 2 is a cubic residue (mod p).

%C It would appear that about two-thirds of the primes have 2 as a cubic residue. A097142/A006880.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicResidue.html">Cubic Residue</a>

%t f[p_] := Block[{k = 2}, While[k < p && Mod[k^3, p] != 2, k++ ]; If[k == p, 0, 1]]; c = 1; k = 2; Do[ While[ p = Prime[k]; p < 10^n, If[ f[p] == 1, c++ ]; k++ ]; Print[c], {n, 5}]

%Y Cf. A006880, A040028.

%K more,nonn

%O 1,1

%A _Robert G. Wilson v_, Jul 26 2004

%E a(6)-a(7) from _Hiroaki Yamanouchi_, Aug 31 2014

%E a(8)-a(12) from _Hiroaki Yamanouchi_, Oct 17 2015