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

[Frank Adams-Watters]

" number of Sophie Germain primes (A005384) between prime(n)^2 and prime(n+1)^2"

I would guess that this is caused by the sizes of prime gaps. A gap of size k between prime(n) and prime(n+1) will produce a gap of size 2k prime(n) + k^2. I don't know what is known about the density of Sophie Germain primes, but 1/log(n)^2 seems likely; the number of Sophie Germain primes in the interval would then be expected to be  on the order of k*prime(n) / log(n)^2, which one would expect to produce the lines.


Franklin T. Adams-Watters


-----Original Message-----
From: Zak Seidov via SeqFan <seqfan at list.seqfan.eu>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Cc: Zak Seidov <zakseidov at mail.ru>
Sent: Sun, Sep 4, 2016 6:34 am
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/