Recurring Digital Invariant

To define a recurring digital invariant of order , compute the sum of the th powers of the digits of a number . If this number  is equal to the original number , then  is called a -Narcissistic number. If not, compute the sums of the th powers of the digits of , and so on. If this process eventually leads back to the original number , the smallest number in the sequence  is said to be a -recurring digital invariant. For example,

			(1)
			(2)
			(3)

so 55 is an order 3 recurring digital invariant. The following table gives recurring digital invariants of orders 2 to 10 (Madachy 1979).

REFERENCES:

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 163-165, 1979.