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Home / $ b_n = c_{n-1} $ (can only append 3 if previous digit is not 3)

$ b_n = c_{n-1} $ (can only append 3 if previous digit is not 3)

February 22, 2026

$$ b_n = c_{n-1} $ (can only append 3 if previous digit is not 3)$

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Let $ a_n = b_n + c_n $, where:
$ b_n $: sequences ending in 3
$ c_n $: sequences ending in 7
$ c_n = a_{n-1} $ (append 7 to any valid sequence)
So $ a_n = b_n + c_n = c_{n-1} + a_{n-1} $, but better to write:
From recurrence:

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