A097142 Number of primes p < 10^n for which 2 is a cubic residue (mod p).

3, 16, 112, 818, 6367, 52299, 442972, 3840740, 33898001, 303369367, 2745366812, 25071938615

Offset: 1

Author

Robert G. Wilson v, Jul 26 2004

Keywords

• more
• nonn

Comments

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

Links

• Eric Weisstein's World of Mathematics, Cubic Residue

Crossrefs

Cf. A006880, A040028.

Programs

Mathematica

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}]

Extensions

a(6)-a(7) from Hiroaki Yamanouchi, Aug 31 2014

a(8)-a(12) from Hiroaki Yamanouchi, Oct 17 2015