“Dudeney number”的意思、由来-开放百科全书

词条

Dudeney number

释义

References
External links

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 six such integers {{OEIS|id=A061209}}:

1	= 1 x 1 x 1	2}}; 1 {{nbsp}} = 1
512	= 8 x 8 x 8	2}}; 8 {{nbsp}} = 5 + 1 + 2
4913	= 17 x 17 x 17	2}}; 17 = 4 + 9 + 1 + 3
5832	= 18 x 18 x 18	2}}; 18 = 5 + 8 + 3 + 2
17576	= 26 x 26 x 26	2}}; 26 = 1 + 7 + 5 + 7 + 6
19683	= 27 x 27 x 27	2}}; 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.

External links

Generalized Dudeney Numbers
Proving There are Only Six Dudeney Numbers

1 : Base-dependent integer sequences

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