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A323474
Array read by antidiagonals: Sprague-Grundy values G_G(n,k) (n>=1, k>=1) for Grossman's game.
1
0, 1, 1, 2, 0, 2, 3, 0, 0, 3, 4, 1, 0, 1, 4, 5, 2, 0, 0, 2, 5, 6, 2, 1, 0, 1, 2, 6, 7, 3, 1, 0, 0, 1, 3, 7, 8, 3, 1, 0, 0, 0, 1, 3, 8, 9, 4, 2, 1, 0, 0, 1, 2, 4, 9, 10, 4, 2, 1, 0, 0, 0, 1, 2, 4, 10, 11, 5, 3, 1, 0, 0, 0, 0, 1, 3, 5, 11, 12, 5, 3, 2, 1, 0, 0, 0, 1, 2, 3, 5, 12, 13, 6, 3, 2, 1, 0, 0, 0, 0, 1, 2, 3, 6, 1
OFFSET
1,4
COMMENTS
Note this has offset 1 whereas A323473 has offset 0.
LINKS
Grant Cairns, Nhan Bao Ho, and Tamás Lengyel, The Sprague-Grundy function of the real game Euclid, Discrete Mathematics 311.6 (2011): 457-462. See Table 2.
FORMULA
G_G(n,k) = floor( |n/k - k/n| ).
EXAMPLE
Array begins:
0, 1, 2, 3, 4, 5, 6, 7, 8, ...
1, 0, 0, 1, 2, 2, 3, 3, 4, ...
2, 0, 0, 0, 1, 1, 1, 2, 2, ...
3, 1, 0, 0, 0, 0, 1, 1, 1, ...
4, 2, 1, 0, 0, 0, 0, 0, 1, ...
5, 2, 1, 0, 0, 0, 0, 0, 0, ...
6, 3, 1, 1, 0, 0, 0, 0, 0, ...
7, 3, 2, 1, 0, 0, 0, 0, 0, ...
8, 4, 2, 1, 1, 0, 0, 0, 0, ...
...
CROSSREFS
Cf. A323473.
Sequence in context: A187881 A344839 A344836 * A132814 A058623 A209689
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 29 2019
STATUS
approved