Smallest value in a sequence

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Given the beginning of a sequence: 59, 106, 37, 58, 89, 145.. find the smallest possible value of this sequence. I know that the answer is '4', but can someone please explain what the rule for this sequence is? thanks!

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Take the sum of the square of the previous number's digits. Once you reach a four it repeats: $4, 16, 37, 58, 89, 145, 42, 20, 4$