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Caterinian numbers

A caterinian number is a natural number, represented as a_n*10^n + a_{n-1}*10^(n-1) + ... + a_1*10 + a_0, for which the sum of the sum of |a_i - a_{n-k}| as k goes from 0 to n and as i goes from 0 to n minus (n+1) is equal to a_0. See caterinian_number.pdf.

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