Just another instance of the (second) [Strong Law of Small Numbers][1]:

We have [A157656][2](n) = [A059100][3](n-1) for all known terms (i.e., $n\leq 6$), but it's also known that A157656(29) > A059100(28). So, the two sequences diverge somewhere.

  [1]: https://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers
  [2]: https://oeis.org/A157656
  [3]: https://oeis.org/A059100