A397052 Consider the Hilbert curve with its cells numbered starting at 0. Two players take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of the other player. Sequence lists cells occupied by the first player.

0, 2, 5, 7, 10, 15, 17, 20, 25, 31, 32, 33, 36, 41, 44, 47, 48, 51, 58, 61, 65, 71, 72, 74, 81, 83, 84, 86, 97, 98, 100, 101, 104, 105, 111, 112, 114, 121, 135, 138, 145, 146, 148, 149, 152, 153, 159, 161, 162, 164, 165, 168, 169, 175, 176, 189, 196, 197, 199

Offset

1,2

Comments

A variant of A392177.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, The cells of the Hilbert curve with x, y <= 2^10 (black pixels correspond to the first player, red pixels to the second player)

Rémy Sigrist, PARI program

Example

The Hilbert curve begins:
    #2---.  #2--#1--#1  #1--#2--#2
         |   |       |   |       |
    #2--#1   .--#1  #2---.   .--#1
     |           |           |
    #2   .---.   .  #1---.   .--#2
     |   |   |   |   |   |       |
    #1---.   .--#2  #1   .--#1--#2
                     |
    #1--#2   .--#1  #1   .---.--#2
     |   |   |   |   |   |       |
    #2  #1---.   .   .---.   .--#1
     |           |           |
    #2--#1   .---.  #1---.  #2--#2
         |   |       |   |       |
    #1--#2   .--#1--#2  #2--#1--#2

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A392177, A397053, A397054, A397055.

Sequence in context: A018483 A018270 A383008 * A080180 A159942 A102339

Adjacent sequences: A397049 A397050 A397051 * A397053 A397054 A397055

Keyword

nonn

Author

Rémy Sigrist, Jun 15 2026

Status

approved