Dudeney number: Difference between revisions
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A '''Dudeney number''' is a positive [[integer]] that is a [[perfect cube]] such that the [[digit sum|sum of its decimal digits]] is equal to the cube root of the number. There are exactly |
A '''Dudeney number''' is a positive [[integer]] that is a [[perfect cube]] such that the [[digit sum|sum of its decimal digits]] is equal to the cube root of the number. There are exactly seven such integers {{OEIS|id=A061209}}: |
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| style="text-align:right;" | 0 || = 0 x 0 x 0 || {{nbsp|2}}; 0 {{nbsp}} = 0 |
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| style="text-align:right;" | 1 || = 1 x 1 x 1 || {{nbsp|2}}; 1 {{nbsp}} = 1 |
| style="text-align:right;" | 1 || = 1 x 1 x 1 || {{nbsp|2}}; 1 {{nbsp}} = 1 |
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Revision as of 22:43, 12 May 2015
A Dudeney number is a positive integer that is a perfect cube such that the sum of its decimal digits is equal to the cube root of the number. There are exactly seven such integers (sequence A061209 in the OEIS):
0 | = 0 x 0 x 0 | ; 0 = 0 |
1 | = 1 x 1 x 1 | ; 1 = 1 |
512 | = 8 x 8 x 8 | ; 8 = 5 + 1 + 2 |
4913 | = 17 x 17 x 17 | ; 17 = 4 + 9 + 1 + 3 |
5832 | = 18 x 18 x 18 | ; 18 = 5 + 8 + 3 + 2 |
17576 | = 26 x 26 x 26 | ; 26 = 1 + 7 + 5 + 7 + 6 |
19683 | = 27 x 27 x 27 | ; 27 = 1 + 9 + 6 + 8 + 3 |
The name derives from Henry Dudeney, who noted the existence of these numbers in one of his puzzles, Root Extraction, where a professor in retirement at Colney Hatch postulates this as a general method for root extraction.
References
- H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1968, p 36, #120.