Recurring Digital Invariant

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,

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

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References

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Cite this as:

Weisstein, Eric W. "Recurring Digital Invariant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RecurringDigitalInvariant.html

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