2, 3, 5, 9, 17, _ What is the next number in the sequence?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

If Japan and Panama decided to merge into a single country, probably people will name it Japanama.

Can you think of two more such country's unions that could produce similar names like Japanama by overlapping their three letters?

John named his first son Alpha, second Beta, third Charlie and fourth Delta. What is the fifth son's name?

Andrew’s doctor gives him three pills and tells him to take one every half hour. How much time will have passed by the time Andrew’s taken all three pills?

You are on a Boat in the mid of a river. You have two cigarettes with you. One of these two you have to light, how will you light the cigarette?

Teacher ask the student

'Why are you standing on that chair in music class ?'.

what did student replied ?

Astrology starts with the alphabet A, Biology starts with B, Psychology with P and Limnology with L.

Can you find an "ology" that begins with a P?

What occurs twice in a week, once in a year but never in a day?