A342882 - OEIS

%I #26 Mar 31 2021 20:27:08

%S 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,

%T 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,

%U 10,10,2,2,2,2,10,10,10,10,11,11,11,11,11,3,3,3,11,11,11,11,11

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

%H Rémy Sigrist, <a href="/A342882/b342882.txt">Table of n, a(n) for n = 0..10009</a>

%H Yuki Irie, <a href="https://doi.org/10.37236/8916">The Sprague-Grundy Functions of Saturations of Misère Nim</a>, Electronic J. Combinatorics, 28(1) (2021), #P1.58.

%H Rémy Sigrist, <a href="/A342882/a342882.png">Colored representation of the array for n, k < 1024</a> (where the color is function of T(n, k), white pixels correspond to zeros)

%H Rémy Sigrist, <a href="/A342882/a342882.gp.txt">PARI program for A342882</a>

%e The first few antidiagonals are:

%e 0, 0,

%e 1, 1, 1,

%e 2, 2, 2, 2,

%e 3, 3, 3, 3, 3,

%e 4, 4, 0, 0, 4, 4,

%e 5, 5, 5, 1, 5, 5, 5,

%e 6, 6, 6, 6, 6, 6, 6, 6,

%e 7, 7, 7, 7, 7, 7, 7, 7, 7,

%e 8, 8, 4, 4, 0, 0, 4, 4, 8, 8,

%e ...

%e The first few rows of the array are

%e .  -, 0, 1, 2, 3, 4, 5, 6, 7, ...

%e .  0, 1, 2, 3, 4, 5, 6, 7, 8, ...

%e .  1, 2, 3, 0, 5, 6, 7, 4, 9, ...

%e .  2, 3, 0, 1, 6, 7, 4, 5, 10, ...

%e .  3, 4, 5, 6, 7, 0, 1, 2, 11, ...

%e .  4, 5, 6, 7, 0, 1, 2, 3, 12, ...

%e .  5, 6, 7, 4, 1, 2, 3, 0, 13, ...

%e .  6, 7, 4, 5, 2, 3, 0, 1, 14, ...

%e .  7, 8, 9, 10, 11, 12, 13, 14, 15, ...

%e .  ...

%e Note that the top left entry in the array is missing.

%o (PARI) See Links section.

%Y Cf. A003987, A342881.

%K nonn,look,tabf

%O 0,6

%A _N. J. A. Sloane_, Mar 30 2021

%E More terms from _Rémy Sigrist_, Mar 31 2021