  Jacobi said "man muss immer umkehren". And indeed it takes a genius like
Michael Somos to take a specific non-linear recurrence, like
a(n)=(a(n-1)a(n-3)+a(n-2)^2)/a(n-4), subject to a(1)=1, a(2)=1, a(3)=1, a(4)=1,
and observe that surprise, surprise, they always generate integers. Then it
takes other geniuses to actually prove this fact (and the more general
so-called Laurent phenomenon).
  But let's follow Jacobi's advise and go backwards. Rather than try to shoot a
target fifty meters away, and most probably miss it, let's shoot first, and
then draw the bull'e eye. Then we are guaranteed to be champion
target-shooters. So let's take a sequence of integers that manifestly and
obviously only consists of integers, and ask our beloved computers to find
non-linear recurrences satisfied by the sequence itself, or by well-defined
subsequences.
