primes in arithmetic progression

[Jonathan Post]

Sorry, I mean: "The semiprime analogue of this is a table that shows the
smallest semiprime S of k (not necessarily consecutive) SEMIprimes in
arithmetic progression
 with common difference d."

On 11/4/06, Jonathan Post <jvospost3 at gmail.com> wrote:
>
> The semiprime analogue of this is a table that shows the smallest
> semiprime S
> of k (not necessarily consecutive) primes in arithmetic progression
> with common difference d (once a 0 appears, the row has ended nonzero
> values):
>
> d   k+1  k=2  k=3  k=4  k=5  k=6  k=7 k=8
> 0   4      4       4      4       4       4       4 ...
> 1   4      9       33    0
> 2   4      4       91    213   1383 8129 3091 0
> 3   4      6       115
> 4   4      6       6      111
> 5   4      4       77
> 6   4      4
> 7   4      14    51
> 8   4      6      6       69
>
> -- Fairly easy to extend, fairly easy to prove the first 0 in a row.
>
> The same can be done for 3-almost primes, 4-almost primes, and so forth,
> this making a 3-dimensional array.
>
>
>
> On 11/4/06, Richard Mathar <mathar at strw.leidenuniv.nl> wrote:
> >
> >
> > Is there an OEIS table that shows the smallest prime p
> > of k (not necessarily consecutive) primes in arithmetic progression
> > with common difference d? The table would look similar to this one
> > below, and contain rather large primes where I am leaving blanks:
> >
> >     k=1 k=2  k=3  k=4  k=5  k=6
> > d
> > 0     2   2    2    2    2    2
> > 2     2   3    3
> > 4     2   3    3
> > 6     2   5    5    5    5
> > 8     2   3    3
> > 10    2   3    3
> > 12    2   5    5    5    5
> > 14    2   3    3
> > 16    2   3
> > 18    2   5    5    5
> > 20    2   3
> > 22    2   7
> > 24    2   5    5   59
> > 26    2   3
> > 28    2   3    3
> > 30    2   7    7    7     7    7
> > 32    2   5
> > 34    2   3    3
> > 36    2   5    7   31
> >
> > The row d=0 and the column k=1 are degenerate and filled with the
> > prime 2. All strides d are even. Example for row d=24 and column k=4:
> > The 4 numbers 59,59+24,59+2*24 and 59+3*24 are all primes.
> >
> > http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primes_AP<http://www.research.att.com/%7Enjas/sequences/Sindx_Pri.html#primes_AP>
> >
> > --Richard
> >
>
>
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