NavList:

Frank, you asked, "how many days are there in an average year when the Moon is never visible while the Sun is in the sky, even for a few minutes, for a mid-latitude observer?"

I replied, “I will write a python/Skyfield program to investigate this over one, or more, 18-year cycles.”

I can now say, Frank,  that the answer to your question is “around 6½”.

In more detail,

1.       For the seven 18.6 years cycles between 1912 and 2043, there will be an average of 6.2 Moonless days/year.  (At 45°S 0°W)

2.       For the 18.6 years ending at the major standstill on 2024/10/09, there will be an average of 6.8 Moonless days/year.  (At 45°N 0°W)

3.       For the 1 year bracketing that major standstill, there were 6 Moonless days.  (At 45°N 0°W.)  There were the same number of days (but different dates) for 0°N and 45°S.

4.       For the 1 year bracketing the last minor standstill in October 2015, there were 4 Moonless days.  (At 45°N 0°W.)  

The next Moonless day, at 45°N 0°W will be on 19^th August with these details.

Sunrise ['2024-08-19 05:06:56Z']

Sunset ['2024-08-19 18:59:16Z']

Moonrise ['2024-08-19 19:14:39Z']

Moonset ['2024-08-19 04:15:18Z']

This event, and all others that I checked, occurred around times of full Moon. Also, I noticed that events were fairly evenly spaced for 0° N, but there was bunching of events at 45°N and 45°S. For example, in 3. above, at 45°N, events occurred on Apr 24, May 23, June 21, June 22, July 21 and Aug 19, with no more before the scan end in April 2025. A run for 45°S for the same dates also gave 6 events, but all between October 2024 and Feb 2025.

I attach the console output for scan 1 above and also my python source code.

Bill