This is essentially the same.

Every positive integer is of the form 3k-2,3k-1, or 3k.

1. If n is of the form 3k-2, then ak has the maximum value
2. If n is of the form 3k-1, then ak = a[k+1] have the maximum value.
3. If n is of the form 3k, then a[k+1] has the maximum value.

It's not hard to prove each of those. Write out the terms with the factorials and powers of 2 for positive j<=k and prove: a[k-j] < ak {and/or a[k+1]} and ak {and/or a[k+1]} > a[k+1+j]

Therefore the answer for the smallest value of n such that a8 will the the maximum value is in cse 2 where

k=8 and If n = 3(8)-1 = 23, then a8 = a[8+1] have the maximum value.

Edwin McCravy