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crontab

the_command runs only on odd days

bash
test $(((`date +%j` % 2))) != 0 && the_command

the_command runs only on odd minutes

bash
test $(((`date +%M` % 2))) != 0 && the_command

the_command runs only on even days

bash
test $(((`date +%j` % 2))) == 0 && the_command

the_command runs only on even minutes

bash
test $(((`date +%M` % 2))) == 0 && the_command