[seqfan] Re: Colorless integers

[William Keith]

On Tue, Feb 22, 2011 at 7:56 PM, N. J. A. Sloane <njas at research.att.com>wrote:

> Start at n, let a(n) be the smallest number in the cycle if it
> goes into a cycle, or -1 if it diverges. Is this sequence
> in the OEIS? and if not, you know what to do!
> Neil
>

Looks like none of them diverge, none go to 0 after 98, and all of them wind
up in a cycle that is fairly close by.  Cycles appear to be exclusively
rooted on multiples of 9: {99, 117, 108, 99}, {198, 216, 207, 198}, {6732,
6750, 6768, 6741, 6759, 6732}, {6822, 6840, 6858, 6831, 6849, 6822}, etc.
Makes sense, as sums of digits will be closed under that property, and I'd
suspect that there's a digital criterion that will tell you where a number
goes.

William Keith