Sorry, I mean: "The semiprime analogue of this is a table that shows the smallest semiprime S<span class="q"> of k (not necessarily consecutive) SEMIprimes in arithmetic progression<br></span>
with common difference d."<br><br><div><span class="gmail_quote">On 11/4/06, <b class="gmail_sendername">Jonathan Post</b> <<a href="mailto:jvospost3@gmail.com">jvospost3@gmail.com</a>> wrote:</span><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
The semiprime analogue of this is a table that shows the smallest semiprime S<span class="q"><br>
of k (not necessarily consecutive) primes in arithmetic progression<br></span>
with common difference d (once a 0 appears, the row has ended nonzero values):<br>
<br>
d k+1 k=2 k=3 k=4 k=5 k=6 k=7 k=8<br>
0 4
4 4
4
4
4 4 ...<br>1 4 9 33 0 <br>
2 4
4 91
213 1383 8129 3091 0 <br>
3 4 6 115<br>
4 4 6 6 111<br>
5 4 4 77<br>
6 4 4<br>
7 4 14 51<br>
8 4 6 6 69<br>
<br>
-- Fairly easy to extend, fairly easy to prove the first 0 in a row.<br>
<br>
The same can be done for 3-almost primes, 4-almost primes, and so forth, this making a 3-dimensional array.<div><span class="e" id="q_10eb43ef55d7ba6b_3"><br>
<br>
<br>
<br><div><span class="gmail_quote">On 11/4/06, <b class="gmail_sendername">Richard Mathar</b> <<a href="mailto:mathar@strw.leidenuniv.nl" target="_blank" onclick="return top.js.OpenExtLink(window,event,this)">mathar@strw.leidenuniv.nl
</a>> wrote:</span><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<br>Is there an OEIS table that shows the smallest prime p<br>of k (not necessarily consecutive) primes in arithmetic progression<br>with common difference d? The table would look similar to this one<br>below, and contain rather large primes where I am leaving blanks:
<br><br> k=1 k=2 k=3 k=4 k=5 k=6<br>d<br>0
2
2 2 2 2 2<br>2 2 3 3<br>4 2 3 3<br>6 2 5 5 5 5<br>8 2 3 3<br>10 2 3 3<br>12 2 5 5 5 5<br>14 2 3 3<br>16 2 3<br>18 2 5 5 5
<br>20 2 3<br>22 2 7<br>24 2 5 5 59<br>26 2 3<br>28 2 3 3<br>30 2
7 7 7
7 7<br>32 2 5<br>34 2 3 3<br>36 2 5 7 31<br><br>The row d=0 and the column k=1 are degenerate and filled with the<br>prime 2. All strides d are even. Example for row d=24 and column k=4:<br>The 4 numbers 59,59+24,59+2*24 and 59+3*24 are all primes.
<br><br><a href="http://www.research.att.com/%7Enjas/sequences/Sindx_Pri.html#primes_AP" target="_blank" onclick="return top.js.OpenExtLink(window,event,this)">http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primes_AP
</a><br><br>--Richard<br></blockquote></div><br>
</span></div></blockquote></div><br>