Convert Integer to Palindrome

Reverse-Append concatenates the digits with their full reverse: 123 → 123 + 321 = 123321 (even-length, 2N digits). Mirror drops the first character of the reverse before appending: 123 → 123 + 21 = 12321 (odd-length, 2N-1 digits). Pick Mirror when you want a centered single-middle-digit palindrome.

Take any number, add its reverse, check if the result is a palindrome. If not, repeat. Most numbers converge quickly: 195 → 195+591=786 → 786+687=1473 → 1473+3741=5214 → 5214+4125=9339 (palindrome in 4 steps). But 196 has been iterated billions of times without ever reaching a palindrome – it’s the smallest suspected “Lychrel number” in base 10.

An integer that has never been proven to reach a palindrome via the Add Reverse process. 196, 295, 394, 493, 592, 689, 691, 788, 790, 879… are the first 10 in base 10. None have been proven to never converge (Lychrel-ness isn’t mathematically settled), but billions of iterations on 196 have produced no palindrome. We cap at 50 iterations and flag any unresolved input.

Direct construction in O(1): take the first half of the digits, mirror them to form a candidate palindrome, then also build two neighbors by bumping the first half ±1. Compare distances to the input. Two boundary candidates (the all-9s number one digit shorter, and the 10…01 number same length) are also considered. The smallest |candidate – input| wins.

Yes. All arithmetic uses BigInt, so a 10-digit input reverse-appended to 20 digits keeps every digit accurate. JavaScript’s regular Number would lose the last 4 digits silently past 2^53 ≈ 16 digits. Try 9999999999 in Reverse-Append mode to see 99999999999999999999 (20 nines, all correct).

Yes. The method runs on the absolute value, and the sign is restored. -12 Reverse-Append → -1221. -196 Add Reverse → flagged Lychrel candidate (the absolute-value math is what matters).

How many digits the output has minus how many the input had. Reverse-Append always doubles the digit count (growth = N). Mirror grows by N-1. Add Reverse can grow significantly across iterations. Nearest typically stays at the same digit count (growth = 0).

No. Everything runs in your browser – just BigInt arithmetic and string operations. Open DevTools → Network and watch zero requests fire after the page loads. Safe for proprietary number sequences or anything private.

Yes. Total bundle is under 20 KB. Once the page loads, disconnect and keep converting. Works on planes, trains, or air-gapped machines.

Beyond the recreational math, palindrome construction is useful for stress-testing string/number reversal code, generating test data for palindrome-check algorithms, and exploring number-theoretic patterns. Computer-science classes use the 196 problem to motivate discussions of unproven conjectures.