# Abacaba D Abacaba

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 \(a + b\).