Find the rule and continue this sequence of digits:
1235813941213533488671216141383377554...
Is there a limit to the number of times in a row a digit can appear?
There is at least one instance of 5 1's in a row in Charlie's printout, but does that create a growing or shrinking pattern?
11111
2222
444
88
16
7
and it dies at 7. With 6 1's in a row we still get a dying pattern, but at least we do end up back at a series of 1's:
111111
22222
4444
888
1616
777
1414
555
1010
111
However, if there was ever a series of 7 1's, we would get a growing pattern which would lead to an infinite number of 1's, 2's, 4's, and 8's in a row:
1111111
222222
44444
8888
161616
77777
14141414
5555555
101010101010
11111111111
7 1's will grow into 11 1's, thereby creating a growing pattern. The following single digit pairs can each create 2 1's: 92, 83, 74, 65.
Addendum: After doing searches on Charlie's printout I find 3 cases of 6 1's in a row. I don't know if there is a repeating pattern going on already which would preclude 7 1's from appearing together, but it seems that the further you go out the more repeated digits you get (duh).
Edited on June 28, 2005, 6:43 pm

Posted by Erik O.
on 20050628 18:36:34 