Zan has created this iterative rule for generating sequences of whole numbers:

1) If a number is 25 or less, double the number.

2) If a number is greater than 25, subtract 12 from it.

Let $F$ be the first number in a sequence generated by the rule above. $F$ is a "sweet number" if 16 is not a term in the sequence that starts with $F$. How many of the whole numbers 1 through 50 are "sweet numbers"?

Let's think step by step and output the final answer within \boxed{}.
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