I just submitted the second sequence (30 terms) to the OEIS.<br>
<br>
-- Ryan<br><br><div><span class="gmail_quote">On 9/7/05, <b class="gmail_sendername">Eric Angelini</b> <<a href="mailto:keynews.tv@skynet.be">keynews.tv@skynet.be</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;">
Hello SeqFan,<br>consider this array where the 1st column is made of all<br>prime numbers, and the nth term of a row is 2 times the<br>previous one on the same row [P(n)=P*2^n]:<br><br> p px2 px4 px8 px16 px32 px64 px128 px256 px512
<br> 2
4 8 16 32
64 128 256 512 1024 ...<br> 3
6 12 24 48
96 192 384 768 1536 ...<br> 5 10
20 40 80 160
320 640 1280 2560 ...<br> 7 14
28 56 112 224
448 896 1792 3584 ...<br> 11 22 44 88 176 352 704 1408 2816 5632 ...<br> 13 26 52 104 208 416 832 1664 3328 6656 ...<br> 17 34 68 136 272 544 1088 2176 4352 8704 ...<br> 19 38 76 152 304 608 1216 2432 4864 9728 ...
<br> 23 46 92 184 368 736 1472 2944 5888 11776 ...<br> 29 58 116 232 464 928 1856 3712 7424 14848 ...<br> 31 62 124 248 496 992 1984 3968 7936 15872 ...<br> 37 74 148 296 592 1184 2368 4736 9472 18944 ...
<br> 41 82 164 328 656 1312 2624 5248 10496 20992 ...<br> 43 86 172 344 688 1376 2752 5504 11008 22016 ...<br> 47 94 188 376 752 1504 3008 6016 12032 24064 ...<br> 53 106 212 424 848 1696 3392 6784 13568 27136 ...
<br> .. ... ... ...<br><br>1) The missing integers in this array are :<br> 1 9 15 18 21 25 27 30 33 35 36 39 42 45 ...<br> ...which (except the first term 1) are A093642.<br><br>2) The main diagonal (NW-SE) reads:<br>
2 6 20 56 176 416 1088 2432 5888 14848 ...<br> ...which is not in the OEIS<br><br>3) Other diagonals (NE-SW) sum up to:<br> 2 = 2<br> (4+3) = 7<br> (8+6+5) = 19<br> (16+12+10+7) = 45<br> (38+24+20+14+11) = 101
<br> (64+48+40+28+22+13) = 215<br><br> ... this is not in the OEIS .<br><br>4) If one keeps only the "primitive terms" of A093642<br> one gets:<br><br> A093642 : 1 9 15 18 21 25 27 30 33 35 36 39 42 45 49 50
<br>"primitives": 1 9 15 .. 21 25 .. .. 33 35 .. 39 .. .. 49 ..<br><br>... and again, this is not in the OEIS :<br> 1 9 15 21 25 33 35 39 49 ...<br><br>If this is of interest, could someone kindly check,<br>compute more terms and enter those sequences in the OEIS?
<br><br>Best,<br>Angelini & Wajnberg<br><br><br></blockquote></div><br>