I find number sequences interesting. More because of their abstractness, their ability to surprise you, the infinite possibilities you need to explore, etc, etc. Basically the aha! factor.
I found one today and was completely baffled. I would not say this is the best "puzzle" and so I am posting solution with the problem but still interesting as it is weird :)
What comes next? 1, 11, 21, 1211, 111221….
Highlight the part between the * symbols for the answer.
* It’s known as Morris Number Sequence. What happens basically is you count the number of times a number appears in the sequence and write in next. So first number is 1 read as one 1 leading to the next number 11, which in turn is two 1. Therefore the next number in sequence is 21. 21 is read as one 2 one 1 leading to the next number in sequence 1211 which is now read as one 1 one 2 two 1 i.e. 111221. Next number becomes 312211 followed by 13112221, 1113213211 & it continues. :) *