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Nice and easy

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  • Jon Perry
    Consider a k-tuple of consecutive positive integers, and define M as max{no.of factors of a_i} The basic conjecture is that if k-tuples with M
    Message 1 of 1 , Sep 2, 2002
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      Consider a k-tuple of consecutive positive integers, and define M as
      max{no.of factors of a_i}

      The basic conjecture is that if k-tuples with M<const exist, then there are
      an infinite number of such k-tuples.

      e.g. consider the 3-tuples, and let the const be 2.

      max{1,2,3}=1
      max{2,3,4}=2 (from the 4=2.2)
      ...
      max{4,5,6}=2

      max(6,7,8)=3 (from 8=2.2.2)

      So the conjecture (k-tuples,const)=(3,2) is, are there an infinite number of
      sequences of 3 consecutive positive integers such that no integer in the
      sequence is more than 2-almost-prime?

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry/maths
      BrainBench MVP for HTML and JavaScript
      http://www.brainbench.com
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