

A301337


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).


3



1, 1, 2, 2, 2, 3, 4, 4, 6, 6, 6, 7, 8, 8, 10, 10, 10, 11, 12, 12
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OFFSET

1,3


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..20.
Dmitry Kamenetsky, Optimal solutions


FORMULA

It seems that for n >= 3:
if n = 0 mod 6, then a(n) = (n/6)*4  1,
if n = 1 or 2 mod 6, then a(n) = floor(n/6)*4,
if n = 3, 4 or 5 mod 6, then a(n) = floor(n/6)*4 + 2.


EXAMPLE

For n = 1, there is only room to search, so a(1) = 1.
For n = 2, the knights search both rooms, so a(2) = 1.
For n = 3, the knights can search the first two rooms twice, so a(3) = 2.
For n = 4 and 5, the knights can search the second and the fourth rooms twice, so a(4) = 2 and a(5) = 2.


CROSSREFS

Cf. A300576, A301426.
Sequence in context: A225499 A215473 A071988 * A302404 A029050 A066920
Adjacent sequences: A301334 A301335 A301336 * A301338 A301339 A301340


KEYWORD

nonn,more


AUTHOR

Dmitry Kamenetsky, Mar 19 2018


STATUS

approved



