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I've created an integer sequence where, after the first two elements, every element is calculated using the previous two. If the first two numbers are $1$ and $3$, the sequence goes as follows:
$$1, 3, 6, 8, 12, 15, 20, 22, 33, 36, 38, 57, 60, 62, 93, 96, 98, 105, 108$$
If the sequence starts wit...