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I have a sequence of numbers like 1,7,22,45,12,96,21,45,65,36,85,14,51,16,18,17,16....65...

IS there any formula to check whether the sequence is random or not ?

In my case

  1. odd numbers are not random since previous+2
  2. even numbers are not random
  3. the numbers can be repeated in a sequence but must be far away,
  4. we cannot generate the sequence using any formula like (x+2)^2 -2x like...
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    And how do you define _random_?2012-09-28
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    @Sasha In my case 1.odd numbers are not random since previous+2 2.even numbers are not random 3.the numbers can be repeated in a sequence but must be far away, 4.we cannot generate the sequence using any formula like (x+2)^2 -2x like...2012-09-28
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    Would the distant digits of $\pi$ count as random - even though they are computable? Randomness is a difficult concept to capture, and is also very important, since the generation of random (or pseudorandom - ie looking random on common tests) numbers is commercially important [think codes and confidential communication]. A readily computable formula or algorithm to identify and predict all pseudorandom sequences would have significant consequences in the real world.2012-09-28
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    Your property 3. is **opposite** to randomness.2012-09-28
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    Maybe this will be of interest: http://en.wikipedia.org/wiki/Diehard_tests2012-09-28

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