

A258756


a(n) = common difference giving the highest score in the game "Sequences" for a sequence with largest element n and as many elements as possible.


0



1, 1, 2, 2, 3, 3, 4, 3, 5, 5, 4, 4, 7, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET

3,3


COMMENTS

The aim of the game is to find, in the given numbered tiles, arithmetic sequences of at least three elements. The score for a sequence is (max element)*(common difference ^ num elements). This sequence gives the common difference which produces the best score for a sequence with largest element n, and containing as many elements as possible.
This sequence converges to 3, which must have something to do with the fact that log(x)/x is maximized at x=e. Is n=45 the last time a(n) is not 3?


LINKS



PROG

(Python)
def score(n, step):
...return n*(step**(n//step+(1 if n%step!=0 else 0)))
.
def best(n):
...return max(range(1, (n1)//2+1), key=lambda step:score(n, step))


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



