# [seqfan] Re: Differenes of conscutive primes

Harvey P. Dale hpd1 at nyu.edu
Thu Jan 13 23:27:24 CET 2011

```	Richard is correct.  The following Mathematica program shows no
gaps from 1 through 69, and I'm fairly confident that expanding the
Range constant will fill in the missing numbers between 69 and 73:

Union[Rest[#/2&/@Differences[Prime[Range[500000]]]]]

Best,

Harvey

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu
[mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Richard Mathar
Sent: Thursday, January 13, 2011 2:46 PM
To: seqfan at seqfan.eu
Subject: [seqfan] Re: Differenes of conscutive primes

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,.
vp>
vp>

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.

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