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palindromeQ[n_Integer] :=
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Block[{digits = IntegerDigits[n]}, digits == Reverse@digits]
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nextNumber[n_Integer] := n + FromDigits[Reverse@IntegerDigits@n]
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lychrelQ[n_Integer] := !
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palindromeQ@
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Catch[Nest[If[palindromeQ[#], Throw[#], nextNumber[#]] &,
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nextNumber[n], 500]]
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