A351043 Lexicographically earliest non-extendable Racetrack trajectory (using von Neumann neighborhood) on spiral on infinite square grid.

0, 1, 9, 24, 46, 45, 21, 6, 4, 15, 33, 32, 12, 11, 10, 8, 7, 5, 16, 36, 63, 97, 96, 60, 13, 27, 50, 80, 119, 165, 164, 116, 75, 41, 68, 66, 64, 99, 141, 140, 138, 93, 55, 86, 84, 49, 79, 78, 76, 43, 69, 104, 102, 100, 143, 193, 192, 190, 137, 57, 54, 52, 25

Offset: 0

Author

Pontus von Brömssen, Jan 30 2022

Keywords

• nonn
• fini
• full

Comments

The car starts at square 0 and thereafter moves, according to the rules of Racetrack with von Neumann neighborhood (see A351042), to the lowest numbered unvisited square. The spiral numbering is described in A316328. After 146 steps, the car cannot move to any unvisited square, so the sequence is finite with 147 terms.

The position of the car after n steps is (A174344(a(n)+1), A274923(a(n)+1)). - Pontus von Brömssen, Jan 30 2025

Links

• Pontus von Brömssen, Table of n, a(n) for n = 0..146
• Pontus von Brömssen, Trajectory of the Racetrack car in A351043.
• Wikipedia, Racetrack

Crossrefs

Cf. A174344, A274923, A316328, A351042.