Find the next element in the list

[Johnx014]

The problem https://i.gyazo.com/66f03e2caa6ee751adc02e3535287e74.png

Find the next element in the list

List 1: 2, 4, 8, 16, 32
List 2: 1, 4, 9, 16, 25
List 3: 1, 4, 7, 10
List 4: J, F, M, A, M, J
List 5: Symbols, see photo

My approaches

List 1: This one seemed obvious. Any given element is the previous element times 2

List 2: Another easy one. It's a list of perfect squares

List 3: I think this one is simple. The next element is the previous element plus 3

List 4: This is where I started to have problems. I thought maybe each letter corresponded with it's place in the alphabet, but this doesn't result in any pattern that I'm able to decipher.
J=10
A= 1
F= 6
M=13
10, 6, 13, 1, 13, 10

List 5: This was the other list that gave me trouble. It seems that the line at the bottom of the first two symbols moves upward. Other than that, I don't see a unifying pattern.

List 6: Forgot to list this one when I first posted.
O, T, T, F, F, S, S, E

 

[HallsofIvy]

For #4, January, February, March, April, May, June, ?

The one just before, which you did not mention, is the same idea: OTTFFSSEN. (123456789)

 

[haruspex]

I would have preferred Halls had not provided the answers straight off. It would have been a gentler hint just to say that each is the initial letters of a standard sequence of words.
For the pictorial one, do you notice a property that all of the pictures share? What happens if you 'undo' that property?

 

[Johnx014]

I would have preferred Halls had not provided the answers straight off. It would have been a gentler hint just to say that each is the initial letters of a standard sequence of words.
For the pictorial one, do you notice a property that all of the pictures share? What happens if you 'undo' that property?

Now I see that all of the pictures are symmetrical. Is it that each figure takes half of the previous figure and realigns it into a new image?

 

[haruspex]

Now I see that all of the pictures are symmetrical. Is it that each figure takes half of the previous figure and realigns it into a new image?

Symmetry is the key, but not in the way you suggest. Since they all exhibit the same symmetry, that symmetry might not be interesting in finding the sequence. How might you 'undo' the symmetry?

 

[Johnx014]

Symmetry is the key, but not in the way you suggest. Since they all exhibit the same symmetry, that symmetry might not be interesting in finding the sequence. How might you 'undo' the symmetry?

Adding to the figure could make it asymmetrical. As would tilting it to move the line of symmetry.

 

[haruspex]

Adding to the figure could make it asymmetrical. As would tilting it to move the line of symmetry.

Not either of those. I carefully said 'undo' rather than 'destroy'. Given some plane figure, how might you give it the bilateral symmetry in these figures without losing any information? (A certain common piece of equipment would do it.)

 

[DEvens]

Heh, somebody here does not watch the Simpsons regularly. Lisa Simpson took an entire episode to get the next in List 5.

Also, it appeared in one of the later seasons of Stargate.

Heh. As long as we are doing brain teasers: Can you think of a sequence of proper English words that would take one minute to speak normally, in which the proper spelling does not include the letter "A"?

 

[haruspex]

Heh. As long as we are doing brain teasers: Can you think of a sequence of proper English words that would take one minute to speak normally, in which the proper spelling does not include the letter "A"?

Interesting, I'd never noticed that. It seems so unlikely, much less than one in a hundred.

 

[DEvens]

Interesting, I'd never noticed that. It seems so unlikely, much less than one in a hundred.

Let me count from one to one hundred: one two three four ... one hundred.

If you speak this in a normal way it will take about one minute. And guess what isn't in there.

 

[haruspex]

Let me count from one to one hundred: one two three four ... one hundred.

If you speak this in a normal way it will take about one minute. And guess what isn't in there.

Yes, I understood. I was trying to indicate that without giving away the answer.