To define a recurring digital invariant of order k, compute the sum of the kth powers of the digits of a number n. If this number n' is equal to the original number n, then n = n' is called a k-Narcissistic number. If not, compute the sums of the kth powers of the digits of n', and so on. If this process eventually leads back to the original number n, the smallest number in the sequence {n, n', n'', ...} is said to be a k-recurring digital invariant. For example, 55:5^3 + 5^3 | = | 250 250:2^3 + 5^3 + 0^3 | = | 133 133:1^3 + 3^3 + 3^3 | = | 55, so 55 is an order 3 recurring digital invariant. The following table gives recurring digital invariants of orders 2 to 10.
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