

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
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OFFSET

0,3


COMMENTS

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^22*n3)).  N. J. A. Sloane, Feb 26 2023


LINKS



EXAMPLE

For starting position (3,0), a 7move 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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



