A342882 Array read by antidiagonals: Sprague Grundy values for two-dimensional Misère Nim game Gamma(P_{Mis}, C^2).

0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 0, 0, 4, 4, 5, 5, 5, 1, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 4, 4, 0, 0, 4, 4, 8, 8, 9, 9, 9, 5, 1, 1, 1, 5, 9, 9, 9, 10, 10, 10, 10, 2, 2, 2, 2, 10, 10, 10, 10, 11, 11, 11, 11, 11, 3, 3, 3, 11, 11, 11, 11, 11

Offset

0,6

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10009

Yuki Irie, The Sprague-Grundy Functions of Saturations of Misère Nim, Electronic J. Combinatorics, 28(1) (2021), #P1.58.

Rémy Sigrist, Colored representation of the array for n, k < 1024 (where the color is function of T(n, k), white pixels correspond to zeros)

Rémy Sigrist, PARI program for A342882

Example

The first few antidiagonals are:
0, 0,
1, 1, 1,
2, 2, 2, 2,
3, 3, 3, 3, 3,
4, 4, 0, 0, 4, 4,
5, 5, 5, 1, 5, 5, 5,
6, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 7, 7,
8, 8, 4, 4, 0, 0, 4, 4, 8, 8,
...
The first few rows of the array are
.  -, 0, 1, 2, 3, 4, 5, 6, 7, ...
.  0, 1, 2, 3, 4, 5, 6, 7, 8, ...
.  1, 2, 3, 0, 5, 6, 7, 4, 9, ...
.  2, 3, 0, 1, 6, 7, 4, 5, 10, ...
.  3, 4, 5, 6, 7, 0, 1, 2, 11, ...
.  4, 5, 6, 7, 0, 1, 2, 3, 12, ...
.  5, 6, 7, 4, 1, 2, 3, 0, 13, ...
.  6, 7, 4, 5, 2, 3, 0, 1, 14, ...
.  7, 8, 9, 10, 11, 12, 13, 14, 15, ...
.  ...
Note that the top left entry in the array is missing.

Prog

(PARI) See Links section.

Crossrefs

Cf. A003987, A342881.

Sequence in context: A111656 A165118 A374013 * A025423 A284263 A087233

Adjacent sequences: A342879 A342880 A342881 * A342883 A342884 A342885

Keyword

nonn,look,tabf

Author

N. J. A. Sloane, Mar 30 2021

Extensions

More terms from Rémy Sigrist, Mar 31 2021

Status

approved