A308884 Follow along the squares in the square spiral (as in A274641); in each square write the smallest nonnegative number that a knight placed at that square cannot see.

0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 3, 3, 2, 0, 1, 3, 2, 1, 0, 3, 3, 3, 2, 0, 1, 3, 3, 1, 0, 0, 0, 3, 3, 0, 0, 0, 2, 1, 3, 3, 0, 0, 0, 2, 2, 3, 2, 0, 0, 0, 2, 1, 3, 3, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 3, 2, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1

Offset

0,8

Comments

Similar to A274641, except that here we consider the mex of squares that are a knight's moves rather than queen's moves.

Since there are at most 4 earlier cells in the spiral at a knight's move from any square, a(n) <= 4.

Links

Table of n, a(n) for n=0..93.

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

N. J. A. Sloane, Beginning of the spiral showing the initial values.

Example

A knight at square 0 cannot see any numbers, so a(0)=0. Similarly a(1)=a(2)=a(3)=0.
A knight at square 4 in the spiral can see the 0 in square 1 (because square 1 is a knight's move from square 4), so a(4) = 1. Similarly a(5)=a(6)=1.
A knight at square 7 can see a(2)=0 and a(4)=1, so a(7) = mex{0,1} = 2.
And so on. See the illustration for the start of the spiral.

Crossrefs

Cf. A274641, A308885-A308895.

Sequence in context: A214211 A099384 A015716 * A101598 A342461 A157129

Adjacent sequences: A308881 A308882 A308883 * A308885 A308886 A308887

Keyword

nonn

Author

N. J. A. Sloane, Jul 01 2019

Status

approved