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Unfortunately this won't happen until October 31st 2600. Starting on March 1st in the year 2600, the Julian calendar (popular in centuries past, and still used in a few places) will differ by 18 days from the Gregorian calendar (the current worldwide standard calendar).
It happens that October 31st in the year 2600 lands on a Friday, and so the Julian October 13th, which lands on that same day, is also a Friday.
There may be a sooner Friday the 13th that lands on Halloween, if you know of other obscure calendars like the Hebrew, Islamic, or Chinese calendars. I don't know enough about those to check.
I love it when people over analyze shitposts. Well done!
It's also always either 5, 6 or 11 years (or 7 in very rare cases, when you're on both sides of a skipped leap year like 1900 or 2100) between "day X falls on day of the week Y" events unless you're talking about February 29.
obscure calendars like the Hebrew, Islamic, or Chinese calendars
That's not very nice to say, also very false
I eagerly await your writeup on whichever calendar you think I need to know more about.
You don't need to learn about other people calendar but you mentionned about 3 calendars that are very famous and used by a significant portion of the world population. That not something obscure at all. Just something that is not part of your culture and you don't know.