A356522 Numbers that are nim cubes; numbers in A335170.

0, 1, 8, 10, 13, 14, 16, 17, 20, 21, 24, 25, 30, 31, 36, 38, 45, 47, 49, 50, 61, 62, 72, 74, 76, 78, 88, 90, 93, 95, 105, 106, 108, 111, 113, 114, 117, 118, 128, 130, 131, 133, 136, 138, 139, 141, 145, 151, 152, 158, 160, 161, 163, 167, 169, 170, 171, 173, 177, 182, 186

Offset: 1

Author

Jianing Song, Aug 10 2022

Keywords

• nonn

Comments

Also numbers in A335172, or numbers that are nim (3*2^m)-th powers for each m.

There are (2^2^k - 1)/3 + 1 terms <= 2^2^k - 1 for each k >= 1. This is because {0,1,...,2^2^k-1} together with the nim operations makes a field isomorphic to GF(2^2^k).

Examples

			8 is a term because (6 N* 6) N* 6 = 5 N* 6 = 8, where N* denotes the nim multiplication.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..21846 (all terms <= 2^2^4 - 1 = 65535)

Crossrefs

Cf. A051175, A335170, A335172. See also A335162 for nim powers.

Programs

PARI

lim(N) = Set(vector(2^2^N, i, A335170(i-1))) \\ A335170 is the function a from Rémy Sigrist in A335170; lim(N) gives all terms <= 2^2^N - 1