Continued fraction for Euler-Mascheroni constant with convergents 0/1, 1/1, 1/2, 4/7, etc., which lie between the monotonically increasing series given by (Sum_{k=1..n} 1/k - Sum_{k=n..n^2} 1/k) and the monotonically decreasing series (Sum_{k=1..n} 1/k - Sum_{k=n..n^2-1} 1/k), both of which converge to gamma. Thus each p/q in the sequence lies within 1/q^2 of gamma.

A178783

Continued fraction for Euler-Mascheroni constant with convergents 0/1, 1/1, 1/2, 4/7, etc., which lie between the monotonically increasing series given by (Sum_{k=1..n} 1/k - Sum_{k=n..n^2} 1/k) and the monotonically decreasing series (Sum_{k=1..n} 1/k - Sum_{k=n..n^2-1} 1/k), both of which converge to gamma. Thus each p/q in the sequence lies within 1/q^2 of gamma.