OK, I arbitrarily declare Bilbo1967 the winner, since he got the more difficult sequences.
The two nobody got were
g) 1, 6, 15, 28, ?
The
Hexagonal Numbers, the next being 45.
and
j) 6, 28, 496, 8128, ?
The
Perfect Numbers, the next being 33550336 (I did say people could look that one up!)
There are only 48 known perfect numbers, and no-one knows whether there are a finite or an infinite number of perfect numbers. It's known that there are at least as many perfect numbers as there are Mersenne Primes, and the corresponding perfect number to each Mersenne Prime is even. It is not known whether there are any odd perfect numbers.