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A342881
Array read by antidiagonals: Sprague Grundy values for two-dimensional Misère Nim game Gamma(P_{Mis}, C_[1]).
2
0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 0, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 0, 5, 5, 5, 6, 6, 3, 1, 1, 3, 6, 6, 7, 7, 7, 6, 0, 6, 7, 7, 7, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 9, 9, 6, 5, 9, 0, 9, 5, 6, 9, 9, 10, 10, 10, 9, 10, 1, 1, 10, 9, 10, 10, 10, 11, 11, 11, 7, 11, 9, 0, 9, 11, 7, 11, 11, 11
OFFSET
0,6
LINKS
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 < 1000 (where the color is function of T(n, k), white pixels correspond to zeros)
EXAMPLE
The first few antidiagonals are:
0, 0,
1, 1, 1,
2, 2, 2, 2,
3, 3, 0, 3, 3,
4, 4, 4, 4, 4, 4,
5, 5, 5, 0, 5, 5, 5,
6, 6, 3, 1, 1, 3, 6, 6,
7, 7, 7, 6, 0, 6, 7, 7, 7,
8, 8, 8, 8, 2, 2, 8, 8, 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, 0, 4, 5, 3, 7, 8, 6, ...
. 2, 3, 4, 0, 1, 6, 8, 5, 9, ...
. 3, 4, 5, 1, 0, 2, 9, 10, 11, ...
. 4, 5, 3, 6, 2, 0, 1, 9, 10, ...
. 5, 6, 7, 8, 9, 1, 0, 2, 3, ...
. 6, 7, 8, 5, 10, 9, 2, 0, 1, ...
. 7, 8, 6, 9, 11, 10, 3, 1, 0, ...
. ...
Note that the top left entry in the array is missing.
PROG
(PARI) See Links section.
CROSSREFS
Cf. A342882.
Sequence in context: A374480 A185617 A250268 * A292137 A292138 A322665
KEYWORD
nonn,look,tabf
AUTHOR
N. J. A. Sloane, Mar 30 2021
EXTENSIONS
More terms from Rémy Sigrist, Mar 31 2021
STATUS
approved