I felt like trying something out, the result is the following number sequence.
Can you guess what it represents? I also created a file with the 2000 first values.
1 | 2 | 3 | 2 | 1 | 2 | 3 | 4 | 2 | 1 | 2 | 3 | 4 | 3 | 2 | 3 | 4 | 5 | 3 | |
2 | 3 | 4 | 5 | 4 | 3 | 4 | 5 | 6 | 4 | 3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 |
2 | 3 | 4 | 5 | 4 | 3 | 4 | 5 | 6 | 4 | 1 | 2 | 3 | 4 | 3 | 2 | 3 | 4 | 5 | 3 |
2 | 3 | 4 | 5 | 4 | 3 | 4 | 5 | 6 | 4 | 3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 |
4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 | 2 | 3 | 4 | 5 | 4 | 3 | 4 | 5 | 6 | 4 |
1 | 2 | 3 | 4 | 3 | 2 | 3 | 4 | 5 | 3 | 2 | 3 | 4 | 5 | 4 | 3 | 4 | 5 | 6 | 4 |
3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 | 4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 |
3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 | 2 | 3 | 4 | 5 | 4 | 3 | 4 | 5 | 6 | 4 |
3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 | 4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 |
5 | 6 | 7 | 8 | 7 | 6 | 7 | 8 | 9 | 7 | 3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 |
2 | 3 | 4 | 5 | 4 | 3 | 4 | 5 | 6 | 4 | 3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 |
4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 | 5 | 6 | 7 | 8 | 7 | 6 | 7 | 8 | 9 | 7 |
4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 | 3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 |
4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 | 5 | 6 | 7 | 8 | 7 | 6 | 7 | 8 | 9 | 7 |
6 | 7 | 8 | 9 | 8 | 7 | 8 | 9 | 10 | 8 | 4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 |
3 | 4 | 5 | 6 | 5 | 4 | 5 | 6 | 7 | 5 | 4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 |
5 | 6 | 7 | 8 | 7 | 6 | 7 | 8 | 9 | 7 | 6 | 7 | 8 | 9 | 8 | 7 | 8 | 9 | 10 | 8 |
5 | 6 | 7 | 8 | 7 | 6 | 7 | 8 | 9 | 7 | 4 | 5 | 6 | 7 | 6 | 5 | 6 | 7 | 8 | 6 |
5 | 6 | 7 | 8 | 7 | 6 | 7 | 8 | 9 | 7 | 6 | 7 | 8 | 9 | 8 | 7 | 8 | 9 | 10 | 8 |
7 | 8 | 9 | 10 | 9 | 8 | 9 | 10 | 11 | 9 | 5 | 6 | 7 | 8 | 7 | 6 | 7 | 8 | 9 | 7 |
Quite easy: http://oeis.org/A006968 :-)
Correct, I did not know that database.