A301426 Number of steps required in the worst case for three knights to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).

1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7, 8, 8

Offset

1,4

Comments

The main entry for this problem is A300576. In this version there are three knights who are searching for the princess; each knight can search a different room.

Links

Table of n, a(n) for n=1..20.

Dmitry Kamenetsky, Optimal solutions

Formula

It seems that for n >= 3:

if n = 3 mod 5, then a(n) = (n - 3)/5*2 + 1,

otherwise a(n) = floor((n - 4)/5)*2 + 2.

Crossrefs

Cf. A300576, A301337.

Sequence in context: A291267 A261221 A080352 * A194222 A025779 A085003

Adjacent sequences: A301423 A301424 A301425 * A301427 A301428 A301429

Keyword

nonn,more

Author

Dmitry Kamenetsky, Mar 21 2018

Status

approved