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A323473
Array read by antidiagonals: Sprague-Grundy values G(n,k) (n>=0, k>=0) for the game of Euclid.
2
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 1, 3, 0, 0, 4, 0, 0, 4, 0, 0, 5, 2, 1, 2, 5, 0, 0, 6, 1, 0, 0, 1, 6, 0, 0, 7, 3, 1, 1, 1, 3, 7, 0, 0, 8, 3, 2, 0, 0, 2, 3, 8, 0, 0, 9, 4, 1, 0, 1, 0, 1, 4, 9, 0, 0, 10, 4, 2, 1, 0, 0, 1, 2, 4, 10, 0
OFFSET
0,8
COMMENTS
Note this has offset 0 whereas A323474 has offset 1. G(0,0) is not defined in Cairns et al., but has been set to 0 here by convention.
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 1.
N. J. A. Sloane, Start of the array (Annotated scanned version of Table 1 of Cairns et al. (2011).)
FORMULA
T(n,k) = floor( |n/k - k/n| ).
EXAMPLE
The first few antidiagonals are:
0;
0, 0;
0, 1, 0;
0, 2, 2, 0;
0, 3, 1, 3, 0;
0, 4, 0, 0, 4, 0;
0, 5, 2, 1, 2, 5, 0;
0, 6, 1, 0, 0, 1, 6, 0;
0, 7, 3, 1, 1, 1, 3, 7, 0;
0, 8, 3, 2, 0, 0, 2, 3, 8, 0;
0, 9, 4, 1, 0, 1, 0, 1, 4, 9, 0;
0, 10, 4, 2, 1, 0, 0, 1, 2, 4, 10, 0;
...
CROSSREFS
Cf. A323474.
Sequence in context: A352562 A362326 A352909 * A341288 A325820 A109042
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 29 2019
STATUS
approved