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Perl 5 -p, 69 bytes 1while$_-=(join'',sort++$\=~/./g)=~s/(.)\1//gr=~y///c<2*$\!~/^.0+$/}{ Try it online!


Brachylog v2, 16 bytes <~l<₁{≜.pX↔Xp}ᵐt Try it online! Borrows Fatalize's ~l trick because my attempt at a ᵘ-based solution is a bit too slow... < The input is less than ~l the length of some list <₁ which is strictly increasing { }ᵐ where each element: ≜. is an ...


Jelly, 14 bytes 1DŒ!ŒḂ×ḢƊ€ẸƲ#Ṫ Try it online! How it works 1DŒ!ŒḂ×ḢƊ€ẸƲ#Ṫ - Main link. Takes an argument n on the left Ʋ - Group the previous 4 links into a monad f(k): D - Convert k to digits Œ! - Permutations of k's digits Ɗ€ - Over each permutation p: ŒḂ - Is p a palindrome? ×Ḣ ...

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