The length of the sequence certainly DOES correlate to the starting number. Certain numbers, such as Mersenne Numbers have sequence lengths that can be predited to within a few percent. Exact length is difficult because part of it appears random and relies on statatics. For instance, the ersenne number 2^177149-1 will diverge for 177149 contiguous steps before starting its "random" phase. But the behavior of "random" patterns can be predicted statistically. My predtiction for that number (over 2.5 million steps) is correct to within a cople percent of the actual runtime. The problem is that different bit patterns have different predictions. But it is simply wrong to say there is no correlation.

The length of the sequence certainly DOES correlate to the starting number. Certain numbers,

ReplyDeletesuch as Mersenne Numbers have sequence lengths that

can be predited to within a few percent. Exact length is difficult because part of it appears random and relies on statatics. For instance, the ersenne number 2^177149-1 will diverge for 177149 contiguous steps before starting its "random" phase. But the behavior of "random" patterns can be predicted statistically. My predtiction for that number (over 2.5 million steps) is correct to within a cople percent of the actual runtime. The problem is that different bit patterns have different predictions. But it is simply wrong to say there is no correlation.

Thanks Paul. I changed the description accordingly.

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