Dudeney Number Checker
Check whether a nonnegative decimal integer equals the cube of the sum of its decimal digits, using exact arithmetic and a 200-character input resource limit.
Description
A Dudeney number equals the cube of its decimal digit sum.
A Dudeney number equals the cube of its decimal digit sum. Digit-sum computation and cubing are exact integer operations.1
The tool returns isDudeney. The indexing and output conventions below determine how to read these values.
When to use Dudeney Number Checker
Use this for the following task: Check whether a nonnegative decimal integer equals the cube of the sum of its decimal digits, using exact arithmetic and a 200-character input resource limit. Use the input and output conventions below to reproduce the intended mathematical quantity.
How to use Dudeney Number Checker and understand its results
- Choose the required indexes, integers or sequence entries. Preserve decimal-string encodings where the field table specifies strings.
- Enter n according to the field table, then run the tool.
- Read isDudeney. A true flag means the candidate meets the stated property; false means it does not.
- If the flag is false, review the candidate and definition. A well-formed nonmember is different from a rejected input.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| n | Nonnegative decimal integer | string (integer/arbitrary); maximum text length 200; pattern ^(0|[1-9][0-9]*)$ | Required |
Read the nonnegative integer as a decimal string, sum its digits with BigInt and compare the cube with the parsed input.
membership ⇔ n=(Σdecimal digits)³ The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| isDudeney | Whether n is the cube of its decimal digit sum | boolean |
{
"input": {
"n": "512"
},
"output": {
"isDudeney": true
}
}Limitations and assumptions
Zero qualifies under this implementation. Leading-zero text and inputs beyond 200 characters are rejected; the tool does not generate all qualifying numbers.
Use the declared integer bounds and string formats. Large exact outputs remain decimal strings; numerical approximations use ordinary floating-point arithmetic. A rejected input is different from a valid zero count or false membership flag.
Alternative or Complementary methods
Choose Münchhausen Digit Self-Power Checker when you need its operation: Check whether n equals the sum of d^d over its decimal digits under an explicit 0^0 convention of zero or one, using exact integers up to 200 input characters. Choose Factorion Checker for the complementary operation: Check whether a nonnegative decimal integer equals the sum of factorials of its digits, including 0!=1 and an input resource limit of 200 characters.
Background reference: OEIS A061209.
References
-
OEIS A061209 — OEIS Foundation
Similar or alternative tools
- Münchhausen Digit Self-Power Checker
Check whether n equals the sum of d^d over its decimal digits under an explicit 0^0 convention of zero or one, using exact integers up to 200 input characters.
- Factorion Checker
Check whether a nonnegative decimal integer equals the sum of factorials of its digits, including 0!=1 and an input resource limit of 200 characters.