Trimorphic Number Checker
Check whether the decimal digits of a nonnegative integer are the final digits of its cube, using exact arithmetic and a 200-character input limit.
Description
A trimorphic integer appears as the final decimal digits of its own cube.
A trimorphic integer appears as the final decimal digits of its own cube. The number’s decimal width determines the modulus needed for the suffix check.1
The tool returns isTrimorphic. The indexing and output conventions below determine how to read these values.
When to use Trimorphic Number Checker
Use this for the following task: Check whether the decimal digits of a nonnegative integer are the final digits of its cube, using exact arithmetic and a 200-character input limit. Use the input and output conventions below to reproduce the intended mathematical quantity.
How to use Trimorphic 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 isTrimorphic. 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 |
Parse a nonnegative decimal string with BigInt, compute its cube and compare the remainder modulo the corresponding power of ten. Zero uses one decimal digit.
trimorphic ⇔ n³ mod 10^digits(n) = n The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| isTrimorphic | Whether n cubed ends in n | boolean |
{
"input": {
"n": "24"
},
"output": {
"isTrimorphic": true
}
}Limitations and assumptions
Only base-ten suffixes are checked. Leading-zero strings and values beyond the 200-character input limit are rejected; no list of all trimorphic numbers is generated.
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 Factorion Checker when you need its 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. Choose Münchhausen Digit Self-Power Checker for the complementary 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.
Background reference: OEIS A033819.
References
-
OEIS A033819 — OEIS Foundation
Similar or alternative tools
- 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.
- 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.