[seqfan] puzzle suitable to make a sequence ?

[Alexander P-sky]

Hello,

Here is the puzzle suitable IMHO to make a sequence ....
Given are the "n" story building and two balls, which are made of some
breakable material (say glass). The balls are such that they break
being thrown down from the certain height (and above), while being
thrown at lesser height, the ball remains to be in tact.
What is the minimum number of throwing attempts "k" is needed to
experimentally but systematically and successfully determine (for the
the worst case scenario ) starting from which floor of the "n" story
building  (if from any) the ball will start to break while being
thrown down. Again it is important to stress that only two balls are
available for experimental testing and that obtaining the definite
result is required.

 I am leaving to the audience (recipients of this list) to come up
with the strategy of determining the minimum number of throwing
attempts "k" for given "n".

Is k(n) sequence in OEIS ?

Regards,
ARP