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

1,3

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).

Links

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A112585 A070479 A335172 * A184116 A319795 A068358

Adjacent sequences: A356519 A356520 A356521 * A356523 A356524 A356525

Keyword

nonn

Author

Jianing Song, Aug 10 2022

Status

approved