A360925 Smallest number of moves needed to win Integer Lunar Lander from starting position (n,0).

0, 1, 4, 7, 9, 12, 14, 17, 19, 21, 24, 26, 29, 31, 34, 36, 38, 41, 43, 46, 48, 50, 53, 55, 58, 60, 63, 65, 67, 70, 72, 75, 77, 79, 82, 84, 87, 89, 92, 94, 96, 99, 101, 104, 106, 108, 111, 113, 116, 118, 120, 123, 125, 128, 130, 133, 135, 137, 140, 142, 145

Offset: 0

Author

Allan C. Wechsler, Feb 25 2023

Keywords

• nonn

Comments

See A360923 for game rules.

Data from Tom Karzes.

The first differences begin 1, 3, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, ... Are all the differences after the start either 2 or 3? - N. J. A. Sloane, Feb 25 2023

Conjecture: For n >= 2, a(n) = n+1+floor(sqrt(2*n^2-2*n-3)). - N. J. A. Sloane, Feb 26 2023

Examples

			For starting position (3,0), a 7-move solution is (2,2), (1,3), (0,3), (-1,2), (-1,1), (-1,0), (0,0). There are no shorter solutions, so a(3) = 7.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..250
• Rémy Sigrist, C++ program

Crossrefs

First column of table A360923.

Cf. A360924, A360926.

Extensions

More terms from Rémy Sigrist, Feb 26 2023