primes in arithmetic progression

[Jonathan Post]

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
>
> --Richard
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20061104/633ecec1/attachment-0002.htm>