1, 3, 7, f, 7, /, DEL, ???

Probably much easier to catch if you were told the sequence written entirely in base 10 is 1, 3, 7, 15, 31, 63, 127 if you don't know different bases, if you are used to lot's of different bases then it's easier as written because you'll notice that they were all the last of the characters for a given common (or not so common) base.

The clue on that one is gonna catch the eye probably for those who are used to hexadecimal, were one counts 1,2,3,4,5,6,7,8,9,a,b,c,d,e,f, 10 and so on. The / and DEL might then catch the eyes of those used to older computer coding, those all represent the last number before ten of a given base, in this case binary, 4, 8, 16, 32, 64, and 128, or 2^n, so that the numbers are 2^n -1 in base 2^n, where n is the position of each clue.

1 ----> 2^1 - 1 in base 2^1 or binary
3 ----> 2^2 - 1 in base 2^2 or 4
7 ----> 2^3 - 1 in base 2^3 or 8
f ----> 2^4 - 1 in base 2^4 or 16

7 ----> 2^5 - 1 in base 2^5 or 32 - Whuh? Yeah base 32 counts 7 as it's last number, which wants a unique character for every number between 0-31, with 32 to be written as 10, goes alphabetically for 26 letters than uses numbers. This character serves more for completeness and to allow confirmation, Base32 is not commonly used.

/ ----> 2^6 - 1 in base 2^6 or 64 - Much like the other, in base64 / is the last unique character used.
DEL----> 2^7 - 1 in base 2^7 or 128 - ASCII, this las tone is actually the best clue, if you see it and have some familiarity with ASCII and hex, you'll take the f and the DEL and realize someone is using increasing bases, which let's you solve backwards and realize what is going on - with tables presumably, I doubt anyone has all those bases memorized though often the last digit of them, their '9' tends to be somewhat familiar

So of course the last is 255, and proceeds 511, 1023, 2047, etc. Extended ASCII (base 256) would probably be the preferred format for the unique character but there are several versions. Personally I consider a pretty good example of why I dislike these sorts of problems. You'd never guess them if you weren't familiar with that sort of thing, and while weird computer bases in powers of 2 were pretty common braniac knowledge for the earlier computer days, it's mostly redundant now. To me it's sort of like measuring intelligence by asking what color a Sith Lord's lightsaber is, you will probably find those who answered red or crimson are above average IQ, but you can't say much about those who said 'Huh?' and those who just guess and guess right probably would make up a big chunk of the right answers.

Edit: By the way the 'somewhat humorous' answer I alluded to in the original question hinges on one of the more common Extended ASCII version using the space character as it's last symbol, so a big blank for an answer, another common one uses a box or square, vaguely alluding to base 2 exponential answers. So, RdrR sort of funny