7 Dec
2005
7 Dec
'05
9:51 p.m.
Here are four more self-descriptive fractal sequences. In each case, each element describes the length and first term of a finite arithmetic sequence. For example, the initial 2 in the first sequence describes the two-term run 2, 3. The following 3s both describe the three-term runs 3, 4, 5. Replace each finite sequence by its length (or its first term) and recover the original infinite sequence. 2, 3, 3, 4, 5, 3, 4, 5, 4, 5, 6, 7, 5, 6, 7, 8, 9, 3, 4, 5, ... 3, 4, 5, 4, 5, 6, 7, 5, 6, 7, 8, 9, 4, 5, 6, 7, 5, 6, 7, 8, ... 4, 5, 6, 7, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, ... 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12, 13, 8, 9, ... Kerry