A360925 - OEIS

%I #17 Feb 26 2023 08:43:18

%S 0,1,4,7,9,12,14,17,19,21,24,26,29,31,34,36,38,41,43,46,48,50,53,55,

%T 58,60,63,65,67,70,72,75,77,79,82,84,87,89,92,94,96,99,101,104,106,

%U 108,111,113,116,118,120,123,125,128,130,133,135,137,140,142,145

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

%C See A360923 for game rules.

%C Data from _Tom Karzes_.

%C 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

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

%H Rémy Sigrist, <a href="/A360925/b360925.txt">Table of n, a(n) for n = 0..250</a>

%H Rémy Sigrist, <a href="/A360925/a360925.txt">C++ program</a>

%e 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.

%o (C++) See Links section.

%Y First column of table A360923.

%Y Cf. A360924, A360926.

%K nonn

%O 0,3

%A _Allan C. Wechsler_, Feb 25 2023

%E More terms from _Rémy Sigrist_, Feb 26 2023