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Definition : $C_s = \{ n \in \mathbb{N} \mid n \text{ reaches 1 in exactly } s \text{ steps in the Collatz sequence, and } n \neq 2^s \}.$
For instance, we have:
$C_5 = \{5\}, \\
C_6 = \{10\}, \\
C_7 = \{3, 20, 21\}, \\
C_8 = \{6, 40, 42\}, \\
C_9 = \{12, 13, 80, 84, 85\}, \\
C_{10} = \{24, 26, 1...