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Home » Subtract sequences missing at least one type: - Sourci

Subtract sequences missing at least one type: - Sourci

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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

📌 $ 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:

📌 $ a_n = a_{n-1} + a_{n-2} $ — standard Fibonacci.

📌 Base cases:

📌 $ n = 1 $: sequences: "3", "7" → both valid → $ a_1 = 2 $

📌 $ n = 2 $: "37", "73", "77", "33" → exclude "33" → 3 valid → $ a_2 = 3 $

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