The Next Number in the Pattern: 312211

[Tom McCurdy]

What row of numbers comes next?

1
11
21
1211
111221
312211
13112221

 

[Gokul43201]

Here's what I see. Except for the first number, all successive numbers have an even number of digits. And I seem to have found some kind of pattern that involves pairing the numbers :

Line 1 = 1
Line 2 = 11 and 1*1 = Line 1
Line 3 = 21 and 2*1 = 1+1, where 1 and 1 are from Line 2
Line 4 = 1222 and (1*2),(1*1) = 2,1 which are from Line 3
Line 5 = 111221 and (1*1), (1*2), (2*1) = 1,2 1+1, and these numbers are in Line 4...
Line 6 = 312211 and (3*1), (2*2), (1*1) = 1+1+1, 2+2, 1; numbers in Line 5
Line 7 = 13112221 and (1*3), (1*1), (2*2), (2*1) = 3,1,2+2,1+1,; numbers in Line 6
This is not a heck of a pattern, but there seem to be some hidden rules for when to add and when not to. I'm not sure if this is going to work forwards...I've been working backwards so far...

So it looks like you add, if the first term in the pair in not 1. ie. (3,1) becomes 1+1+1 but (1,3) becomes 3. This seems to be the way to generate repetitions. Okay, I think I've got it !

3,1 means there are three 1's while 1,3 means there is one 3 !

This seems to work throughout - for all the lines. So, for instance, in line 4 : 1211 means there's one 2 and one 1 in the previous line.

Then Line 8 should be : one 1, one 3, two 1's, three 2's and one 1 OR 1113213211

NICE !

 

[Tom McCurdy]

1113213211
is correct

good work

I will find another riddle or make one up to post in a day or so.