A323473 Array read by antidiagonals: Sprague-Grundy values G(n,k) (n>=0, k>=0) for the game of Euclid.

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

Table of n, a(n) for n=0..77.

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

Adjacent sequences: A323470 A323471 A323472 * A323474 A323475 A323476

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jan 29 2019

Status

approved