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

0,3

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..250

Rémy Sigrist, C++ program

Example

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.

Prog

(C++) See Links section.

Crossrefs

First column of table A360923.

Cf. A360924, A360926.

Sequence in context: A048973 A092861 A248561 * A007072 A186323 A007064

Adjacent sequences: A360922 A360923 A360924 * A360926 A360927 A360928

Keyword

nonn

Author

Allan C. Wechsler, Feb 25 2023

Extensions

More terms from Rémy Sigrist, Feb 26 2023

Status

approved