Array with primes

[Ryan Propper]

And the third was just submitted as well.

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