My Math Forum Statistics : sequence adjustment

 September 8th, 2008, 09:16 AM #1 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Statistics : sequence adjustment Hi, I have found a sequence of 584 numbers, each number is associated with a function that gives me a prime number. Let us call n(i) a number of my sequence U(n) i=0 to 583. Let us call P(n(i)) a defined function where the output is always a primer number. Here is my sequence Link : http://rapidshare.de/files/40425321/seq584.txt.html I need your help to find a line ax+b such as 90 per cent or more of its integer points match my sequence. The correlation ratio is 0.998 When I tried a diagram of U(n) it seems like a perfect line. I was really surprised to see such alignment. I want to understand if there is something new to exploit. If I can express all the n(i) as linear function it will be good even if some points do not match my sequence. Thank you for any help
 September 8th, 2008, 09:23 AM #2 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: Statistics : sequence adjustement The link is not working So here is the sequence 1 10 17 19 31 32 35 52 56 58 59 95 109 121 127 148 149 163 164 169 185 211 217 236 238 250 253 275 278 290 295 301 302 305 307 323 326 344 382 413 416 418 419 430 439 458 470 472 479 497 508 509 523 524 529 548 560 569 587 610 619 631 650 652 655 677 692 694 697 698 709 742 766 781 788 815 818 830 835 839 850 856 857 908 922 946 962 989 1004 1007 1022 1042 1046 1133 1153 1195 1199 1222 1244 1249 1261 1265 1282 1313 1319 1333 1334 1408 1420 1423 1424 1429 1445 1448 1460 1462 1481 1514 1591 1598 1600 1604 1625 1649 1660 1667 1682 1718 1735 1757 1772 1777 1790 1799 1808 1883 1888 1919 1930 1931 1937 1978 1991 1993 2015 2038 2039 2053 2059 2099 2101 2126 2165 2180 2239 2258 2270 2291 2296 2306 2320 2341 2386 2387 2413 2435 2452 2492 2503 2504 2509 2545 2560 2561 2566 2630 2635 2671 2677 2690 2693 2698 2699 2725 2740 2741 2761 2768 2780 2788 2789 2812 2837 2852 2875 2902 2905 2920 2921 2942 2944 2960 2965 2969 2980 3005 3029 3061 3112 3130 3133 3139 3158 3196 3203 3224 3229 3287 3314 3350 3352 3355 3359 3377 3403 3440 3442 3445 3460 3461 3466 3511 3530 3556 3557 3578 3593 3598 3620 3641 3661 3667 3680 3710 3712 3719 3752 3754 3757 3758 3770 3773 3790 3793 3796 3800 3802 3820 3827 3841 3860 3863 3865 3869 3880 3934 3955 3973 4033 4058 4075 4096 4103 4162 4186 4214 4238 4259 4271 4277 4292 4300 4304 4309 4321 4325 4349 4367 4382 4411 4418 4450 4457 4498 4499 4508 4525 4529 4612 4652 4654 4690 4700 4702 4726 4741 4742 4748 4769 4832 4907 4943 4961 4982 4985 4987 5002 5003 5009 5048 5069 5080 5131 5135 5150 5171 5197 5200 5221 5225 5228 5245 5281 5288 5318 5350 5356 5374 5378 5399 5405 5408 5420 5425 5441 5558 5593 5609 5626 5711 5732 5750 5821 5824 5860 5911 5930 5972 5974 5975 5995 6014 6031 6052 6097 6104 6109 6142 6160 6161 6167 6215 6250 6271 6277 6295 6298 6308 6320 6347 6367 6383 6389 6410 6412 6415 6419 6436 6454 6458 6502 6520 6544 6581 6610 6611 6631 6653 6671 6694 6697 6701 6721 6722 6745 6748 6749 6766 6782 6787 6811 6812 6839 6851 6874 6877 6904 6928 6940 6943 6962 6985 7028 7049 7060 7061 7066 7081 7084 7111 7115 7132 7157 7172 7174 7190 7225 7240 7310 7312 7315 7319 7351 7358 7379 7393 7420 7421 7426 7465 7481 7486 7510 7517 7550 7576 7643 7712 7730 7735 7739 7750 7774 7775 7823 7825 7840 7885 7886 7919 7931 7933 7957 7970 7994 8011 8018 8051 8072 8074 8140 8167 8185 8210 8219 8237 8251 8278 8300 8342 8344 8347 8368 8386 8410 8417 8431 8450 8453 8459 8476 8492 8497 8501 8528 8540 8545 8587 8614 8633 8651 8672 8674 8675 8701 8720 8746 8764 8780 8810 8815 8830 8854 8875 8891 8893 8900 8908 8966 8989 9008 9025 9029 9046 9047 9088 9089 9119 9191 9202 9221 9265 9268 9281 9316 9332 9358 9359 9376 9406 9440 9443 9514 9530 9572 9577 9590 9592 9602 9607 9608 9629 9640 9641 9646 9662 9710 9713 9718 9719 9733 9755 9770 9797 9799 9800 9803 9820 9826 9884 9934 9937 9952 9995
September 8th, 2008, 06:01 PM   #3
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Quote:
 Originally Posted by momo I need your help to find a line ax+b such as 90 per cent or more of its integer points match my sequence.
The best you can get with any line is 12 points, which is just over 2%.

 September 8th, 2008, 07:07 PM #4 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: Statistics : sequence adjustment Thank you for your comment. 12 points I still do not understand why all 584 values seem aligned. http://rapidshare.de/files/40428815/graph1.JPG.html
 September 8th, 2008, 09:43 PM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Statistics : sequence adjustment Yes, 12 points with a line of slope 18. The values are all close to a line, but the line wiggles enough that you can't hit more than 12 at a time (by my calculation). If 'close enough' suffices you can use a least-squares fit -- but if you need exact you're out of luck.
 September 9th, 2008, 06:10 AM #6 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: Statistics : sequence adjustment Hi, Why all the values are in the same "line"? Now, it seems that I have some explanation. If we take any line (ax+b) and we try to find out the nearest values to each point it will be easy to find prime numbers. a=2 b=5 I tried it for one thousand values it shows me a "perfect line". Thank you for your help.
September 9th, 2008, 09:06 AM   #7
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Quote:
 Originally Posted by momo If we take any line (ax+b) and we try to find out the nearest values to each point it will be easy to find prime numbers. a=2 b=5 I tried it for one thousand values it shows me a "perfect line".
You mean that there are many primes of the form 2n + 5 for 1 <= n <= 1000? I count 301, which seems about right.

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