# [seqfan] Re: Differences of consecutive primes

Neil Fernandez primeness at borve.org
Thu Jan 13 21:33:59 CET 2011

```In message <201101131946.p0DJkKR4006432 at dommel.strw.leidenuniv.nl>,
Richard Mathar <mathar at strw.leidenuniv.nl> writes
>
>http://list.seqfan.eu/pipermail/seqfan/2011-January/006863.html
>
>vp> From seqfan-bounces at list.seqfan.eu Thu Jan 13 20:05:16 2011
>vp> From: "Veikko Pohjola"
>vp> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>vp>
>vp> Consider the halved differences of consecutive primes
>(Prime[k+1]-Prime[k])/2, k=2,3,4,.,K. Remove the duplicates and sort to obtain
>an ordered set {1,2,3,.,a(i)}of all natural numbers from 1 to a(i). The allowed
>numbers a(i) make up the following sequence: a(i) = 1, 2, 3, 4, 7, 17, 18,.

>My impression from http://oeis.org/A000230 is that this sequence of halved
>prime gaps is dense, and does not miss numbers in the range 8 to 16.

If I understand Veikko correctly, the suggested sequence can also be
expressed as a(n)=b(n)/2 where b(n) is the sequence:

prime gaps for which, when they first occur, all smaller even numbers
have already appeared as prime gaps

Best regards,

Neil

--
Neil Fernandez

```