A360924 Smallest number of moves needed to win Integer Lunar Lander with starting position (0,n).

0, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18

Offset

0,2

Comments

See A360923 for game rules.

Data provided by Tom Karzes.

It appears that a(n) = 1 + floor(sqrt(4*n-3)) for n>0 (which is essentially A000267 and A027434). - N. J. A. Sloane, Feb 25 2023 [This is proved by Casteigts, Raffinot, and Schoeters (2020) in the form a(n) = ceiling(2*sqrt(n)). - Pontus von Brömssen, Mar 01 2023]

Links

Tom Karzes, Table of n, a(n) for n = 0..484

Arnaud Casteigts, Mathieu Raffinot, and Jason Schoeters, VectorTSP: A Traveling Salesperson Problem with Racetrack-like acceleration constraints, arXiv:2006.03666 [cs.DS], 2020. See Lemma 7.

Example

From (0,6), a 5-move solution is (-1,5), (-2,3), (-2,1), (-1,0), (0,0). There is no shorter solution, so a(6) = 5.

Crossrefs

Top row of table A360923. Cf. A360925, A360926.

See also A000267 and A027434.

Sequence in context: A318994 A261101 A327704 * A027434 A319434 A174697

Adjacent sequences: A360921 A360922 A360923 * A360925 A360926 A360927

Keyword

nonn

Author

Allan C. Wechsler, Feb 25 2023

Status

approved