A143344 vs A080092

[Richard Mathar]

Well, that's a good side-effect of trying to connect sequences into
supersequences and arrays.  Errors are detected in the existing seqs.
So instead of a new seq (unless someone cares about k=4, k=5, k=6) we
have correction by Franklin T. Adams-Watters to A031131, and comments
that "The main diagonal is A072473, and the array is A090321" for
A001223 and A031131 and A031165 and A072473 and A090321?

On Thu, Aug 14, 2008 at 9:52 PM,  <franktaw at netscape.net> wrote:
> ... The main diagonal is A072473, and the array is A090321
> (by descending anti-diagonals from this presentation).
>
> Franklin T. Adams-Watters
>
> -----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..
>