# Array generalizing A031165

franktaw at netscape.net franktaw at netscape.net
Fri Aug 15 06:52:05 CEST 2008

```... The main diagonal is A072473, and the array is A090321
(by descending anti-diagonals from this presentation).

-----Original Message-----
From: franktaw at netscape.net
...
And the n = 1 column is A040976.

In fact, the entire second row is off by one column; the 3 needs to be
inserted at the beginning of the row.

-----Original Message-----

From: Jonathan Post <jvospost3 at gmail.com>

Since I see that A031165 has just been (re)edited, and comments
already read: "This sequence is the k=3 case of the family of
sequences a(k,n) = prime(n+k) - prime(n). See A001223 and A031131 for
k = 1 and 2."  it seems to me worth looking at the array a(k,n) =
prime(n+k) - prime(n) by value (rather than just by reference). Is
there anbything worth saying about it, or worth entering it as a seq
by antidiagonals?

.......|n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|...
k=1.|...1..|...2...|...2...|...4..|...2...|...4...|...
k=2.|...4..|...6...|...6...|...6..|...6...|...6...|...
k=3.|...5..|...8...|...8...|..10.|...8...|..10..|...
k=4.|...9..|..10..|..12...|..12..|.12..|..16..|...
k=5.|..11.|..14..|..14...|..16..|.18..|..18..|...
k=6.|..15.|..16..|..18...|..22..|.20.|...24..|...

and so forth..

The n=1 column is 1,4,5,9,11,15,... which is not in OEIS..

Is the OEIS sequence A143344 a duplicate of A080092?

http://research.att.com/~njas/sequences/?q=id:A143344|id:A080092

```