[seqfan] Re: A173897: Quasi-linear patterns in graph

Zak Seidov zakseidov at mail.ru
Sun Sep 4 17:10:13 CEST 2016


Yes! Just look at graph of  A069482 :



a(n) = prime(n+1)^2 - prime(n)^2.


>Воскресенье,  4 сентября 2016, 17:05 +03:00 от "David Wilson" <davidwwilson at comcast.net>:
>
>Suppose the SG primes to have a slowly decreasing density d(n) around n (like the density 1/log(n) for primes).
>a(n) counts the number of SG primes on the interval [p(n) ^2, p(n+1)^2], with p(n) = nth prime.
>So we will have
>
>a(n) 
>=~ d(p(n)^2) * (p(n+1)^2 - p(n)^2)
>= d(p(n)^2) * (p(n+1) + p(n)) * (p(n+1) - p(n))
>=~ d(p(n)^2) * 2p(n) * (p(n+1) - p(n))
>
>The first two factors change relatively smoothly, the last factor is the prime gap, and fluctuates more or less randomly between positive even integers.
>So each of the kth "line" in the plot of a(n) likely includes the elements a(n) where the prime gap (p(n+1) - p(n)) = 2k.
>
>> -----Original Message-----
>> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Zak
>> Seidov via SeqFan
>> Sent: Sunday, September 04, 2016 7:34 AM
>> To: Sequence Fanatics Discussion list
>> Cc: Zak Seidov
>> Subject: [seqfan] A173897: Quasi-linear patterns in graph
>> 
>> Any idea about quasi-linear patterns in graph of A173897?
>> --
>> Zak  Seidov
>> 
>> --
>> Seqfan Mailing list -  http://list.seqfan.eu/
>
>
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>Seqfan Mailing list -  http://list.seqfan.eu/



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