How to run a crontab each Sunday, except is it's first day of the month

I'm running a weekly backup every Sunday and it's working fine. Additionally I'm running a new monthly backup every 1st of each month, meaning if the 1st of the month is a Sunday, I got double backups. My crontab file :

* 0 1 * * backup_monthly.sh
* 0 2-31 * 0 backup_weekly.sh

My expectations are that backup_monthly is running the first of each month no matter what, and backup_weekly, every Sunday except Sunday 1st

Problem is that backup_weekly is running daily in this scenario

I did some research didn't find any occurrence with a negative condition.

Thanks if you have some idea

Solution

0 0 * * * ([ "$(date +\%d)" = "01" ] || [ "$(date +\%a)" = "Sun" ]) && backup_monthly.sh

What does it mean?

0 0 * * * means the cron job will run at 12:00 AM (midnight) every day.
([ "$(date +\%d)" = "01" ] || [ "$(date +\%a)" = "Sun" ]) consists of two parts.
- [ "$(date +\%d)" = "01" ] checks if the current day of the month is 01.
- [ "$(date +\%a)" = "Sun" ] checks if the current day of the week is Sun.
&& backup_monthly.sh specifies the command that will be executed.

So, the cron job is scheduled to run every day at 12:00 AM, but the backup command will be executed only if it's either the 1st day of the month or Sunday.