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Haskell, 56 bytes f a=a:f(a+g(read.pure<$>show a)) g a=minimum a+maximum a Try it online!
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# [Haskell], 56 bytes <!-- language-all: lang-hs --> f a=a:f(a+g(read.pure<$>show a)) g a=minimum a+maximum a [Try it online!][TIO-kt1iux21] [Haskell]: https://www.haskell.org/ [TIO-kt1iux21]: https://tio.run/##y0gszk7Nyfn/P00h0TbRKk0jUTtdoyg1MUWvoLQo1UbFrjgjv1whUVOTKx2oIDczLzO3NFchUTs3sQLC@p@bmJmnYKuQm1jgq6BRUJSZV6JXkpidqmBkqpemqRBtqKdnaBD7HwA "Haskell – Try It Online"