[seqfan] Re: Patarn in Prime related sequence

Giovanni Resta g.resta at iit.cnr.it
Wed Sep 9 09:37:02 CEST 2015


On 09/09/2015 06:37 AM, zbi74583.boat at orange.zero.jp wrote:
>      Hi,Seqfans
>      See the graph of A096447
>
>      I think that a property of primes looks like a random sequence.
>      But almost linear sequences appear in the graph.

I found the thing quite natural.

It's like a random walk that starts in position 0 and at each step
goes randomly left or right. You collect the step numbers at which you
are again at 0.

When you are near zero it is reasonable to "oscillate" near that 
position and thus reach zero several times. When you take a walk quite 
far from 0 then on the average you have to spend more time to reach 0 
again. So I find it not surprising to have cluster of near values (thus 
small differences) separated by large gaps.

by the way, I extended this sequence to 10000 terms in the b-file.

Giovanni





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