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Home » Stop Your Brain from Exploding: The Wrath of Cortex Stuns Fans Online! - Sterling Industries

Stop Your Brain from Exploding: The Wrath of Cortex Stuns Fans Online! - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 $T_n$: ending in exactly one 2 (i.e., last is 2, previous ≠ 2)

📌 $U_n$: ending in exactly two consecutive 2s (i.e., last two are 22, but not 222)

📌 Recurrences:

📌 $S_n = S_{n-1} + T_{n-1} + U_{n-1}$ (append 3 to any valid string)

📌 $T_n = S_{n-1}$ (append 2 to a string ending in 3)

📌 $U_n = T_{n-1}$ (append 2 to a string ending in exactly one 2)

📌 Initial conditions ($n=1$):

📌 $S_1 = 1$ (string: 3)

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