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%I #14 Mar 24 2024 11:40:44
%S 1,1,2,2,2,3,4,4,6,6,6,7,8,8,10,10,10,11,12,12
%N Number of steps required in the worst case for two knights to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).
%C The main entry for this problem is A300576. In this version there are two knights who are searching for the princess; each knight can search a different room.
%H Dmitry Kamenetsky, <a href="/A301337/a301337.txt">Optimal solutions</a>
%F It seems that for n >= 3:
%F if n = 0 mod 6, then a(n) = (n/6)*4 - 1,
%F if n = 1 or 2 mod 6, then a(n) = floor(n/6)*4,
%F if n = 3, 4 or 5 mod 6, then a(n) = floor(n/6)*4 + 2.
%F i.e., a(n) = A302404(n-2).
%e For n = 1, there is only room to search, so a(1) = 1.
%e For n = 2, the knights search both rooms, so a(2) = 1.
%e For n = 3, the knights can search the first two rooms twice, so a(3) = 2.
%e For n = 4 and 5, the knights can search the second and the fourth rooms twice, so a(4) = 2 and a(5) = 2.
%Y Cf. A300576, A301426.
%K nonn,more
%O 1,3
%A _Dmitry Kamenetsky_, Mar 19 2018
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