- #1

bahamagreen

- 1,014

- 52

I did this initiating the process with the first 66 positive integers and found some cycles:

160->217->352->160

250->133->55->250

and I found these four that terminate themselves or any others if they appear (1 is trivial)

153

370

371

407

For the first 66 I got 18 "153"s so .2727... maybe approaching 1/3, but more suspiciously like 1/4...

I looked around OEIS and saw this process as the base 10 third power version of the Narcissistic/Plus Perfect/Armstrong numbers... and found these four numbers to be the only ones for "n"=3 where an "n" digit number is the sum of the "n"th powers of its digits.

Is there an analytical approach to determine the 1/3 claim for 153?