Eric Angelini:
Start with (my date of birth) for instance: 1951 This in "p"; now make the absolute differences between p's digits, from left to right, like this: 1-9 = 8 9-5 = 4 5-1 = 4 1-1 = 0 (this is the last digit of "p" minus the first one) You then get "q" = 8440.
if q > p add q to p and iterate if q < p subtract q from p and iterate
1951 yields: {1951, 10391, 24071, 48832, 8320, 3192, 321, 209, 506, 1067, 2683, 6934, 3322, 3221, 2209, 1912, 10723, 28235, 94358, 43127, 30974, 70205, 142457, 464583, 243232, 32122, 21021, 9810, 8091, 17078, 84795, 41552, 7520, 5193, 331, 309, 705, 1457, 4583, 3232, 2121, 1010, 2121, ...}, so {1010, 2121}, a small loop. There are loops of assorted lengths but a difficulty in compiling them is that even some small numbers (like 199 which apparently loops to {30, 63}, if I've done this correctly) take their time in getting to them: http://chesswanks.com/num/AddSubtractIterate.txt