24 lines
1.2 KiB
Plaintext
24 lines
1.2 KiB
Plaintext
The digital root, <math>X</math>, of a number, <math>n</math>, is calculated:
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: find <math>X</math> as the sum of the digits of <math>n</math>
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: find a new <math>X</math> by summing the digits of <math>X</math>, repeating until <math>X</math> has only one digit.
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The additive persistence is the number of summations required to obtain the single digit.
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The task is to calculate the additive persistence and the digital root of a number, e.g.:
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:<math>627615</math> has additive persistence <math>2</math> and digital root of <math>9</math>;
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:<math>39390</math> has additive persistence <math>2</math> and digital root of <math>6</math>;
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:<math>588225</math> has additive persistence <math>2</math> and digital root of <math>3</math>;
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:<math>393900588225</math> has additive persistence <math>2</math> and digital root of <math>9</math>;
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The digital root may be calculated in bases other than 10.
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;See:
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* [[Casting out nines]] for this wiki's use of this procedure.
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* [[Digital root/Multiplicative digital root]]
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* [[Sum digits of an integer]]
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* [[oeis:A010888|Digital root sequence on OEIS]]
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* [[oeis:A031286|Additive persistence sequence on OEIS]]
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* [[Iterated digits squaring]]
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<br><br>
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