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 Post subject: Math/physics teasers
PostPosted: Wed Nov 21, 2012 1:59 pm 
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These are the first 100 numbers of an (infinite) row of numbers:

2 47 109 185 253 357 425 505 607 677
3 55 115 191 283 361 433 515 613 687
7 59 117 193 285 369 445 529 617 695
11 61 131 203 299 375 451 535 623 701
13 67 137 211 301 379 463 539 631 719
19 73 143 213 313 391 471 545 637 721
25 87 145 229 319 395 477 557 647 731
31 91 157 239 333 397 487 563 661 757
37 97 167 241 351 415 499 587 665 761
41 103 171 247 355 419 501 601 675 769

Which are the next 20 numbers in this row ? The logic behind is pure mathematics. For the record: the millionth number in the row is 22395195.

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 Post subject: Re: Math/physics teasers
PostPosted: Wed Nov 21, 2012 2:29 pm 
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The next 20 numbers in the series are:
787
789
799
803
817
827
841
847
859
865
875
877
883
895
901
911
929
949
953
967

I wonder why you presented them top to bottom and then left to right, instead of left to right and then top to bottom...

Skarabajo.

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 Post subject: Re: Math/physics teasers
PostPosted: Wed Nov 21, 2012 2:40 pm 
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Location: Bay Area, California
mixer wrote:
These are the first 100 numbers of an (infinite) row of numbers:

2 47 109 185 253 357 425 505 607 677
3 55 115 191 283 361 433 515 613 687
7 59 117 193 285 369 445 529 617 695
11 61 131 203 299 375 451 535 623 701
13 67 137 211 301 379 463 539 631 719
19 73 143 213 313 391 471 545 637 721
25 87 145 229 319 395 477 557 647 731
31 91 157 239 333 397 487 563 661 757
37 97 167 241 351 415 499 587 665 761
41 103 171 247 355 419 501 601 675 769

Which are the next 20 numbers in this row ? The logic behind is pure mathematics. For the record: the millionth number in the row is 22395195.

Isn't this sequence the prime (irreducible) polynomials with x^n powers where n is the nth LSB bit as a coefficiont then written vertically into columns with 10 rows? Just like what you'd use with CRC or many aspects of cryptography?

The next two columns would be:

787 875
789 877
799 883
803 895
817 901
827 911
841 929
847 949
859 953
865 967

So 787 in binary is 1100010011 which is ? 1*x^9 + 1*x^8 + 0*x^7 + 0*x^6 + 0*x^5 + 1*x^4 + 0*x^3 + 0*x^2 + 1*x^1 + 1*x^0

? factor(1*x^9 + 1*x^8 + 0*x^7 + 0*x^6 + 0*x^5 + 1*x^4 + 0*x^3 + 0*x^2 + 1*x^1 + 1*x^0)
% = [x^9 + x^8 + x^4 + x + 1 1]

EDIT: fixed the polynomial example.

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 Post subject: Re: Math/physics teasers
PostPosted: Wed Nov 21, 2012 3:27 pm 
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Location: Belgium
Well I have no idea if your answers are correct, someone send me this problem and I did not find the solution yet! :wink:
I'll send a mail and ask him...........

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 Post subject: Re: Math/physics teasers
PostPosted: Thu Nov 22, 2012 2:30 am 
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Yes correct !
Congratulations! :D

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