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September 8th, 2008, 10:16 AM   #1
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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
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September 8th, 2008, 10:23 AM   #2
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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
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September 8th, 2008, 07:01 PM   #3
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Re: Statistics : sequence adjustment

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%.
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September 8th, 2008, 08:07 PM   #4
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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
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September 8th, 2008, 10:43 PM   #5
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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.
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September 9th, 2008, 07:10 AM   #6
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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.
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September 9th, 2008, 10:06 AM   #7
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Re: Statistics : sequence adjustment

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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