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A360925 Smallest number of moves needed to win Integer Lunar Lander from starting position (n,0). 4
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 (list; graph; refs; listen; history; text; internal format)
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, 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.
Sequence in context: A048973 A092861 A248561 * A007072 A186323 A007064
KEYWORD
nonn
AUTHOR
Allan C. Wechsler, Feb 25 2023
EXTENSIONS
More terms from Rémy Sigrist, Feb 26 2023
STATUS
approved

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Last modified May 26 10:56 EDT 2024. Contains 372824 sequences. (Running on oeis4.)