- #1
bahamagreen
- 1,014
- 52
I found reference to a function described as taking the digits of a natural number and summing their third powers, iterating the process. The claim was that 1/3 of all natural numbers will terminate the process in 153.
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?
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?