Keith Number Checker
Check whether a decimal integer of at least two digits reappears in the recurrence seeded by its digits and summing the previous digit-count terms; input is capped at 10¹².
Description
A Keith number reappears in a recurrence initialized by its decimal digits.
A Keith number reappears in a recurrence initialized by its decimal digits. Each later term sums as many preceding terms as the original digit count.1
The tool returns isKeith. The indexing and output conventions below determine how to read these values.
When to use Keith Number Checker
Use this for the following task: Check whether a decimal integer of at least two digits reappears in the recurrence seeded by its digits and summing the previous digit-count terms; input is capped at 10¹². Use the input and output conventions below to reproduce the intended mathematical quantity.
How to use Keith 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 isKeith. 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 integer (resource limit 10^12) | integer; minimum 0; maximum 1000000000000 | Required |
Exclude integers below ten. Use a BigInt circular buffer of digits and a rolling sum, advancing until the sum reaches or exceeds the candidate.
digit-seeded next term = sum of preceding digitCount terms The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| isKeith | Whether n is a nontrivial Keith number | boolean |
{
"input": {
"n": 197
},
"output": {
"isKeith": true
}
}Limitations and assumptions
The input is at most 10¹². Single-digit numbers are excluded by convention, and the tool returns membership without the generated recurrence.
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 Dudeney Number Checker for the complementary operation: 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.
Background reference: OEIS A007629.
References
-
OEIS A007629 — 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.
- 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.