term or phrase representing a placeholder or variable

How can I express in standard American English that events occur "every X days" or end "after X occurrences" — here, "X" is a placeholder for a variable and unknown quantity — without using "X" or another single-character term?

I considered using the phrase "every so many days" or "after so many occurrences", but I fear that this is a colloquialism that may not be clear to all concerned.

The context is a set of web form drop-down menus in which we allow people to choose the basis for how they schedule recurring events. I've looked at how standard calendaring software handles this, but their solutions are not ideal for persons with low vision or blindness.

given number of

or

specified number of

after a given number of days

every specified number of days

I would suggest number of.

To use it your example: "Every (number of) days". This lets the user know you are looking for an integer and is more than a single letter.