What comes next in this sequence?

The Game Room
1

Just a quick one that some people might enjoy. Yes, I know you can come up with a formula/justification for pretty much any number to come next in any sequence, but that’s not the point. The real question is, is this a ‘fair’ puzzle, i.e. is it possible to work out the answer that I’m thinking of if you haven’t seen it before?

The sequence is: 4, 8, 12, 2, 1, 6, 7, 3, 5…

Hint: This sequence has a limited number of terms.

Bigger hint: There are only a total of 12 terms in the sequence.

I’ll post my answer next week, once people have had a chance to give it a try.

2

The next one is 11. And you have 6 and 7 switched.

July is before June.

3

Oops, you’re quite right of course.

Corrected sequence: 4, 8, 12, 2, 1, 7, 6, 3, 5…

4

Show of hands: Was anyone else’s first reaction to look this up in the Online Encyclopedia of Integer Sequences?

5

Why am I not surprised, though faintly disappointed, to find out such an online resource exists?

6

Why disappointed? It’s a valuable research tool.

7

I know, but I can imagine its use as a method of avoiding having to think out such things for one’s self when assigned to do so.

I do see that the database was started in 1965 by a grad student interested in combinatorics, so that’s pretty cool.

8

I did Google it before posting as I didn’t know if it was a well-known puzzle - looked to me like it wasn’t, but the OEIS hit didn’t come up for some reason (and yes, when I Googled I did have the numbers in the right order!).

9

8, 7, 5, 10, 11, 13, 8, 7, 14, 19, 20, 22, ?

eta: And if you look it up, it is in the OEIS.

10

I doubt anyone’s waiting around here for the answer I promised given the strong hint spoilered in post 2, and the references to OEIS, but I am a man of my word, so: it’s the months of the year (represented by their numerical designation) listed in alphabetical order, so the sequence in the post 3 ends with 11, 10, 9.

11

Here’s the answer to mine:

1
2
4
8
16 - 1+6=7
32 - 3+2=5
64 - 6+4=10
128 - 1+2+8=11
256 - 2+5+6=13
512 - 5+1+2=8
1024 - 1+2+4=7
2048 - 2+4+8=14
4096 - 4+9+6=19
8192 - 8+1+9+2=20
16384 - 1+6+3+8+4=22
32768 - 26
65536 - 25
131072 - 14
262144 - 19
524288 - 29
1048576 - 31
2097152 - 26

As I noted above, this sequence is not new. But I did independently invent it on my own. I like the way it develops; rising but not steadily.