I tried iterated reverse and subtraction on those numbers in the first two tables. For example 196-691=-495-594=-1089-9801=-10890-9801=-20691-19602=-40293-39204=-79497. You also get this palindrome from doing the same to 1012.

Also 1012 x 37=37444. Do an IRS on that result and you also get -79497. 79497/73 (reverse of 37) = 1089

1012 is an example of a monodrome. A palindrome is when the difference between the outer and successive inner pairs of digits is 0. In a monodrome it's 1. An interesting pandigital monodrome is 8642013579.

I'm also interested in emergent numerical behaviour when you get into the negative side of Fibonacci style sequences, particularly ones with recurrences a(n) = a(n-1)+a(n-m) where m>2. There they swing wildly (so kind of bounce) from positive to negative values like a chaotic pendulum. Could you point me to any literature?

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