A324274 a(n) is the number of squares visited by a single pawn move for an even square and a double pawn move for an odd square on a diagonally numbered board and moving to the lowest available unvisited square of different parity at each step from subsequent starting squares n; or a(n) = 0 for an infinite length.

20, 0, 8, 17, 6, 9, 4, 7, 0, 11, 16, 5, 18, 0, 10, 19, 8, 19, 8, 11, 12, 25, 6, 9, 6, 9, 0, 13, 24, 7, 20, 7, 20, 0, 12, 15, 24, 21, 26, 21, 10, 21, 10, 13, 14, 27, 8, 27, 8, 11, 8, 11, 0, 15, 16, 33, 22, 9, 22, 9, 22, 9, 22, 0, 14, 17, 32, 23

Offset: 1

Author

Jan Koornstra, Feb 20 2019

Keywords

• nonn

Comments

It is conjectured that all starting squares will either have a finite length or reach the top row of the board at square 2 first and then follow the sequence for a(2) to infinity. A324275 contains numbers n for which A324274(n) = 0.

Examples

			a(1) is the length of A324273. a(2) has an infinite length as it will follow a repeating pattern along the top row of the numbered board.
		

Crossrefs

Cf. A316588, A324273, A324275.