Eric Angelini:
18 enters in the loop 18-36-72-144-(18)
A small quibble: Since the doubling appears to be part of "the procedure", I make that: 18, 36, 72, 144, 36, ..., so I would represent the loop portion as {36, 72, 144}, putting the smallest member of the loop first. There are loop members, and loop precursors that run into loops, and I take 18 as one of the latter. Trivially, I think we can add a zero to the end of each member of a loop to turn it a new loop; for example, {360, 720, 1440}. So far, I have nine non-trivial loops (assuming that I have done things correctly) and put them here: http://chesswanks.com/num/iterate(2*iterate(SumAdjacentIdenticalDigits)).txt They are introduced by [smallest precursor, loop length]. Additionally, I have marked the largest loop member with an asterisk. Allan Wechsler:
I think 178 is the smallest element of a 24-step loop.
Except for my quibble, yes.