A393236 - OEIS

%I #27 May 08 2026 09:22:39

%S 1,2,3,4,5,4,5,4,5,4,5,4,5,6,5,6,7,8,7,8,9,10,11,12,13,14,15,16,15,16,

%T 15,16,15,16,17,18,19,18,19,18,19,18,19,20,19,20,19,20,19,20,19,20,19,

%U 20,19,20,19,20,19,20,19,20,19,20,19,20,19,20,19,20

%N Consider the square spiral with its cells numbered starting at 0. Two players, Black and Red, take turns. When it is Black's turn, he places a knight at the smallest unoccupied cell not attacked by an existing Red knight, and when it is Red's turn, she places a knight at the smallest unoccupied cell not attacked by an existing Black knight. a(n) gives the number of pieces among the first n with a record index when placed, minus the others.

%H Rémy Sigrist, <a href="/A393236/b393236.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A393236/a393236.png">Scatterplot of the first 1000000 terms</a>

%H Rémy Sigrist, <a href="/A393236/a393236.gp.txt">PARI program</a>

%F a(n+2) >= a(n).

%e The first terms are:

%e   n   a(n)  |A395355(n-1)|  Record?

%e   --  ----  --------------  -------

%e    1     1               0  Yes

%e    2     2               1  Yes

%e    3     3               2  Yes

%e    4     4               3  Yes

%e    5     5               5  Yes

%e    6     4               4  No

%e    7     5               9  Yes

%e    8     4               6  No

%e    9     5              11  Yes

%e   10     4              10  No

%e   11     5              15  Yes

%e   12     4              12  No

%e   13     5              20  Yes

%e   14     6              24  Yes

%e   15     5              21  No

%o (PARI) \\ See Links section.

%Y Cf. A392177, A395355, A395818.

%K nonn

%O 1,2

%A _Rémy Sigrist_, May 07 2026