There is, in fact, only two other limit cycles besides the one starting at 11; the repeated patterns are [0] and [14, 5, 9]. The underlying state machine only has 100 states, and it isn't hard to analyse the whole thing. My sloppy diagram covers less than half a page. On Wed, Oct 24, 2012 at 7:22 AM, Eric Angelini <Eric.Angelini@kntv.be>wrote:
I guess this is old hat (at least for the Fibonacci Quarterly);
What could be the longest repeated pattern in a sequence where we just add the last two digits to produce the next term? Starting with 0,1, produces: 0,1,1,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,11,... where the repeated pattern is = [2,3,5,8,13,4,7,11] This pattern is 8-term long (or 10-digit long). Could one find a longest pattern with another start? Best, É.
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