Category:Recurring Digital Invariants

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This category contains results about Recurring Digital Invariants.
Definitions specific to this category can be found in Definitions/Recurring Digital Invariants.

Let $k \in \Z_{>0}$ be a positive integer.

Let $f: \Z_{>0} \to \Z_{>0}$ be the mapping defined as:

$\forall m \in \Z_{>0}: \map f m = $ the sum of the $k$th powers of the digits of $n$.


Let $n_0 \in \Z_{>0}$ be a positive integer.

Consider the sequence:

$s_n = \begin{cases} n_0 & : n = 0 \\ \map f {s_{n - 1} } & : n > 0 \end{cases}$

If:

$\exists r \in \N_{>0}: s_r = n_0$

then the smallest of the terms $n_0, n_1, \ldots, n_r$ is a recurring digital invariant of order $k$.

Subcategories

This category has the following 2 subcategories, out of 2 total.