number of digits
Everyone sees that the numbers in the sequence grow larger.
But it takes a mathematical view to ask yourself if there's any rule in this growth.
Let's count the number of digits for each element of the sequence.
The growth becomes more clear if we graph more elements and use a logaritmical scale for the vertical axis.
| number | element | digits |
| 1 | 1 | 1 |
| 2 | 11 | 2 |
| 3 | 21 | 2 |
| 4 | 1211 | 4 |
| 5 | 111221 | 6 |
| 6 | 312211 | 6 |
| 7 | 13112221 | 8 |
After some elements, it's clear that the growth factor isn't random at all.
Using a logaritmical scale for the vertical axis an increasing trend line means:
- the number of digits in the sequence grows exponentially
- the proportion of two consecutive elements is constant