On the sum of \(k\)th powers of each digit of an integer (Q2724944)
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scientific article; zbMATH DE number 1618455
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the sum of \(k\)th powers of each digit of an integer |
scientific article; zbMATH DE number 1618455 |
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28 July 2002
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alternant number
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digital properties
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0.9415159
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On the sum of \(k\)th powers of each digit of an integer (English)
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Given a positive integer \(A_0=\sum^t_{i=0} 10^ia_i\), where \(0\leq a_i\leq 9\), let \(A_1=\sum^t_{i=0} a_i^k\). In general, letting \(A_n\) be the sum of the \(k\)th powers of the digits of \(A_{n-1}\), the author proves that the sequence \(\{A_n\}\) must be cyclic from some term on.
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