Latest Series Riddles

Next in sequence is 13112221.

This series describes each number that came before it:
1 [One]
11 [One One]
21 [Two One(s)]
1211 [One Two and One One(s)]
111221 [One One, One Two, and Two One(s)]
312211 [Three One(s), Two Two(s), and One One]

The next number in the series is:
13112221 [One Three, One One, Two Two(s), Two One(s)]

N for November!

794

The nth term in the series is given by the sum of x^n for x in the range 1 to 3, i.e. 1^n + 2^n + 3^n.

Thus the first term is 1^1 + 2^1 + 3^1 = 1 + 2 + 3 = 6,
the second term is 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14,
and so on.

The sixth term is then 1^6 + 2^6 + 3^6 = 1 + 64 + 729 = 794.

The letters are the first letters of the words in the question. Thus, the next two letters are A and W.

61
Reversed digits of squares of number in descending order.

129.

These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1

Fm.

These are the chemical elements whose atomic numbers are perfect squares.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

60. 100 years in a century, 365 days in a year, 24 hours in a day, 60 minutes in an hour, & 60 seconds in a minute.

Each word rhymes with its numeric position in the list. (e.g. 'gun' rhymes with 'one', etc.)

'2'
This single sequence in fact consists of two sequences: the first sequence is 2-3-4-5-... and the second sequence is 9-18-36-72-... . To make the puzzle harder, all digits have been placed apart. Conclusion: the next term in the sequence is a '2'.