Add Kaprekar number checker to special_numbers

[Sean-Randall]

This PR adds a new function is_kaprekar_number(n) under maths/special_numbers/.

The function determines whether a number is a Kaprekar number based on digit-splitting logic, where the square of a number is divided into two parts that sum to the original number. It includes inline doctests to demonstrate usage and ensure correctness.

✔️ This contribution follows all repository contribution guidelines:

• Type hints included (n: int -> bool)
• File and function names follow lowercase conventions
• Clean formatting per PEP8
• Validated locally using doctest.testmod()

🎯 Educational Value:
This function enhances the repository's coverage of special number classifications and provides a clean, beginner-friendly example of digit-based number theory in Python.

Tested and ready for review. Thank you for maintaining this valuable resource!

[mindaugl]

Shouldn't 10 be a Kaprekar number, since 10^2 = 100, and "100" = "10" + "0" gives 10?

[Sean-Randall]

Shouldn't 10 be a Kaprekar number, since 10^2 = 100, and "100" = "10" + "0" gives 10?

https://cs.uwaterloo.ca/journals/JIS/VOL3/iann2a.html#:~:text=For%20each%20n%20%3E%3D%201%20%2C,)%20when%20N%20%3D%2010n%20.

10 is Disallowed, see above.

[mindaugl]

Shouldn't 10 be a Kaprekar number, since 10^2 = 100, and "100" = "10" + "0" gives 10?

https://cs.uwaterloo.ca/journals/JIS/VOL3/iann2a.html#:~:text=For%20each%20n%20%3E%3D%201%20%2C,)%20when%20N%20%3D%2010n%20.

10 is Disallowed, see above.

Thanks for the link. Then, the definition should be clarified in the code function description to be: "Kaprekar numbers: positive numbers n such that n = q+r and n^2 = q*10^m+r, for some m >= 1, q >= 0 and 0 <= r < 10^m, with n != 10^a, a >= 1." (https://oeis.org/A006886)?

[Sean-Randall]

Shouldn't 10 be a Kaprekar number, since 10^2 = 100, and "100" = "10" + "0" gives 10?

https://cs.uwaterloo.ca/journals/JIS/VOL3/iann2a.html#:~:text=For%20each%20n%20%3E%3D%201%20%2C,)%20when%20N%20%3D%2010n%20.
10 is Disallowed, see above.

Thanks for the link. Then, the definition should be clarified in the code function description to be: "Kaprekar numbers: positive numbers n such that n = q+r and n^2 = q*10^m+r, for some m >= 1, q >= 0 and 0 <= r < 10^m, with n != 10^a, a >= 1." (https://oeis.org/A006886)?

Updated the function to align with the strict definition of Kaprekar numbers per OEIS A006886 and Iannucci (1997). Powers of 10 are now explicitly excluded. Let me know if there's anything else to improve!

[mindaugl]

It seems this check is not needed anymore.

[mindaugl]

Just added a comment in code, as the check for int(right) == 0 seems not to be necessary any more after adding explicit check for powers of 10.

[Sean-Randall]

Just added a comment in code, as the check for int(right) == 0 seems not to be necessary any more after adding explicit check for powers of 10.

Thanks! I removed the int(right) == 0 check as suggested. The new logic excludes powers of 10 directly. Let me know if anything else needs a tweak.

[algorithms-keeper]

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🔗 Relevant Links

Repository:

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• Formatted string literals (f-strings)
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• unittest
• pytest

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[algorithms-keeper]

Please provide descriptive name for the parameter: n

[Sean-Randall]

All checks are now passing, including tests, Ruff style checks, and namespace packaging. The implementation follows the strict Kaprekar definition and excludes powers of 10 as required. Everything should be ready for merge. Thanks again for the helpful feedback!

[cclauss]

@priya-sundaram-dev This algorithm is the first Kaprekar PR, and it has pytests instead of doctests (which is OK with me as long as they pass in CI). Is this or one of the four below the best implementation that we should merge?

• Add Kaprekar's Constant (6174) Algorithm to Special Numbers #13862
• maths/special_numbers: add Kaprekar number #14563
• maths: add Kaprekar number implementation #14562
• Kaprekar numbers implementation with doctests #15048

[priya-sundaram-dev]

Thanks for the ping, @cclauss. I read all five and verified the two strongest against OEIS A006886 (canonical Kaprekar numbers ≤ 10000 — both reproduce the sequence exactly, no extras/misses).

One clarification first: #13862 is a different algorithm — it's Kaprekar's constant (the 6174 routine), not the Kaprekar-number predicate. It's not really a duplicate of the other four and could stand on its own merits separately.

That leaves four true is_kaprekar_number candidates. My ranking:

1. maths: add Kaprekar number implementation #14562 (@Eraol) — my recommendation. Cleanest of the set: pure-integer arithmetic split via %/// (no string parsing), and the right > 0 guard is the mathematically correct way to exclude powers of 10 (10→100 splits to 10+00, rejected because the right part is zero). Concise (~56 lines), doctests cover 1/9/45/55/2223, negatives, and a 1.5 TypeError. ✅ verified against OEIS.
2. maths/special_numbers: add Kaprekar number #14563 (@Kcstring) — also correct, good doctests, but ~104 lines and raises ValueError on non-positive input where a boolean predicate returning False reads more naturally.
3. This PR Add Kaprekar number checker to special_numbers #12723 (@Sean-Randall) — logic is correct (✅ verified against OEIS), but it uses math.log10(number).is_integer() to detect powers of 10, which leans on float precision (fine in this range, but the right > 0 integer guard sidesteps it entirely), and it ships pytest tests where the repo prefers doctests.
4. Kaprekar numbers implementation with doctests #15048 (@VishalNyk) — adds an arbitrary-base parameter; nice generalization but ~173 lines is more surface area than the "one clear educational example" ethos wants.

So: I'd merge #14562 for the checker, and consider #13862 separately as the distinct 6174-routine algorithm. Kudos to everyone — this was a close call between #14562 and #14563.