What is a "semester series" for eclipse prediction? - Solar saros series 147 and 152
Any eclipse is a coincidence of a new or full moon (repeating every 29.53 day lunation or synodic month)
and a lunar node (moon crossing the ecliptic, repeating every 27.21 day draconic month).
A semester
is 6 synodic months, close enough to 6.5 draconic months that eclipses can occur at that interval in a series 3 or 4 years long.

The interval between any two solar or lunar eclipses can be expressed as $aI + bS$,
where $S$ is the saros interval of 223 lunations,
$I$ is the inex interval of 358 lunations between adjacent saros series,
and $a$ and $b$ are integers.
The semester interval of 6 lunations is $5I - 8S$; for each eclipse in saros $n$, there may be an eclipse in saros $n-5$ one semester earlier, an eclipse in saros $n+5$ one semester later, or both.
As the eclipses in a given saros series are about 18 years apart, each is in a different semester series.

For example, one semester series runs from 2015 to 2018 and includes one solar eclipse in each of saros series 120, 125, 130, 135, 140, 145, 150, and 155.
Another runs from 2018 to 2021 and includes one solar eclipse in each of saros series 117, 122, 127, 132, 137, 142, 147, and 152.