# Abacaba D Abacaba

Level pending

Consider the infinite sequence A001511 in OEIS described as follows:

1: $$*1*$$
2: $$1, *2*, 1$$
3: $$1, 2, 1, *3*, 1, 2, 1$$
4: $$1, 2, 1, 3, 1, 2, 1, *4*, 1, 2, 1, 3, 1, 2, 1$$
$$...$$
$$\infty : 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, ...$$

The Cesaro Summation of this sequence (the limit of the arithmetic mean as more terms are taken into account) can be expressed as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. Evaluate $$a + b$$.

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