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9,73,241,561,1081,1849,_?_

algebra.com

31–40 of 91 posts

Re: 9,73,241,561,1081,1849,_?_

#32

This question is not well-defined. Any number can be a solution.

This question is not well-defined.

It's defined just well enough to identify you as someone who'd rather debate the problem than attack it. In other words, it has done its job.

Re: 9,73,241,561,1081,1849,_?_

#33
post #14

This question is not well-defined. Any number can be a solution.

Here's one interpretation: What will the simplest program that outputs these numbers output next?

The simplest program that outputs these numbers is the program that outputs these numbers, so it doesn't output anything next.

Re: 9,73,241,561,1081,1849,_?_

#36
This method of computing successive terms of a polynomial actually has an interesting place in the history of computers; the basic principle is the same as that used by Charles Babbage's difference engine.

Wikipedia article on the difference engine: http://en.wikipedia.org/wiki/Difference_engine

Just for fun, a difference engine built with Legos: http://acarol.woz.org/

Re: 9,73,241,561,1081,1849,_?_

#37

I discovered difference tables as a kid, didn't know they were used much, I was modelling motion on a 2D display (an oscilloscope hooked to a P2P11!). Was a lifesaver for quick polynomial evolution - uses only addition, execution time scales linearly with the order of the polynomial. So, how do you go from the difference table "coefficients" to the polynomial?

Integrate the constant 48 back to the series level:

  48 -> 48x -> 24x^2 -> 8x^3
Subtract 8x^3 from the series

  9 - 8•1^3, 73 - 8•2^3, 241 - 8•3^3
and repeat the whole process on this series for the coefficient of x^2, etc...

Re: 9,73,241,561,1081,1849,_?_

#38
post #14

Earlier quoted context omitted.

Here's one interpretation: What will the simplest program that outputs these numbers output next?

The simplest program that outputs these numbers is the program that outputs these numbers, so it doesn't output anything next.

  python -c 'print 9,73,241,561,1081,1849
  # or better yet
  echo 9,73,241,561,1081,1849

Re: 9,73,241,561,1081,1849,_?_

#39

Earlier quoted context omitted.

The simplest program that outputs these numbers is the program that outputs these numbers, so it doesn't output anything next.

python -c 'print 9,73,241,561,1081,1849 # or better yet echo 9,73,241,561,1081,1849

You forgot the 'output next', bit of the question ;)

Re: 9,73,241,561,1081,1849,_?_

#40
I loaded into excel, then copy and dragged down to see what excel would say is the next 2 answers ... I got the following

...1081,1849,[1890.067],[2248.467].... Now I just wonder how excel got these answers :/

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