With the following JavaScript calculator a nearly infinite number of eclipse cycles can be generated. The lengths of each period is given in days (mean solar), Gregorian-, Julian-, and Egyptian years, 12-month (Islamic) lunar years, 235-month Metonic cycles, weeks, 60-day cycles and 260-day Tzolkin cycles.
Also listed are the mean angular shift (in degrees) of the Moon’s position with respect to the lunar node and the mean angular shifts (modulo 360°) in the lunar and the solar anomaly. Ideally, all three shifts should be as small as possible as one would then obtain long eclipse cycles in which eclipses repeat under nearly similar circumstances.
The eclipse cycle calculator allows you to account for secular changes in the luni-solar orbital elements (adopted from Meeus (1998), chapter 49) by changing the epoch. Although the lengths of the repeat periods of the eclipse cycles themselves hardly change, the life expectancies of some of them can dramatically change.
While the life expectancy of the Saros cycle slowly decreases as time passes by, the life expectancy of the Inex cycle steadily increases and appears to become infinitely long around AD 6035. However, second-order changes in the lengths of the cycles involved will in this particular case limit the actual life expectancy.
The optimum inex/saros ratio for long-lasting eclipse cycles also changes with time: around 2000 BC it was close to 6, at the begin of the Christian era it had risen to 8, at present it is about 12 and it still continues to rise with ever increasing speed until it will become infinitely large around AD 6035.