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Home » \(x - 3 = 0 \Rightarrow x = 3\) - High Altitude Science

\(x - 3 = 0 \Rightarrow x = 3\) - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Now, subtract those that do **not** contain two consecutive 3s (i.e.,...
Let $ a_n $ be the number of $ n $-digit sequences of 3 and 7 with no...
This is a Fibonacci-type recurrence:
Let $ a_n = b_n + c_n $, where:
$ b_n $: sequences ending in 3
$ c_n $: sequences ending in 7
$ 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:

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