Sloane's A046459 has an article on Dudeney numbers, which are integers equal to sum of the digits of their cubes.
For example: 18
3=5832, and 5+8+3+2=18. Accordingly, 18 is a Dudeney number.
The said article lists 0,1,8,18,26, and 27 as all possible Dudeney numbers.
A Dudezero number is a base 10 nonnegative integer the digits of whose cubes are each reduced by 1 and the said integer is equal to the sum of transformed digits.
For example, 5 is a Dudezero number, since:
5
3=125, and:
(1-1)+(2-1)+(5-1)=5
Determine all possible Dudezero numbers.
The concept of Dudezero numbers is defined where the digits of a base 10 non-negative integer are each reduced by 1, and the sum of these transformed digits is equal to the original integer. While the example of 5 seems to satisfy this
legit nursing essay service condition, the logic breaks down for larger numbers.
For instance, let's consider the number 11. Here's the breakdown:
1^3 - 1 = 0
1^3 - 1 = 0
The sum of the transformed digits (0 + 0) is 0, which wouldn't equal the original number (11) as required for a Dudezero number.
Similarly, you can analyze other two-digit and three-digit numbers to find that the transformed digits' sum would always be less than the original number. Therefore, it seems unlikely that there exist any Dudezero numbers under the given definition.
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