Loading ...
Sorry, an error occurred while loading the content.

Composite integer function

Expand Messages
  • Kermit Rose
    You might be interested in the following two variable function. Define F(m,k) recursively as follows. F(1,1) = 15 F(m+1,k) = F(m,k) + 4*(2*m + k + 2) F(m,k+1)
    Message 1 of 2 , Nov 17, 2009
    • 0 Attachment
      You might be interested in the following two variable function.

      Define F(m,k) recursively as follows.

      F(1,1) = 15
      F(m+1,k) = F(m,k) + 4*(2*m + k + 2)
      F(m,k+1) = F(m,k) + 2*(2*m + 1)

      Then for both m and k positive integers,
      F(m,k) = (2 * m + 1) * (2 * m + 2 * k + 1)

      which makes it evident that every odd non-square positive composite
      integer appears in the table, and that no prime appears in the table.

      This function could be used to make an efficient prime number sieve.

      Note that F(m,0) = (2*m+1)**2


      Factoring a positive integer z is equivalent to finding it in the table.
    • Yann Guidon
      Hello Kermit, it seems that my emails can t reach you due to some unexplainable blacklist on some router near you. So I answer on the list : ... ... can
      Message 2 of 2 , Nov 18, 2009
      • 0 Attachment
        Hello Kermit,

        it seems that my emails can't reach you
        due to some unexplainable blacklist on some router near you.
        So I answer on the list :

        Kermit Rose wrote:
        > You might be interested in the following two variable function.
        <snip>
        > Factoring a positive integer z is equivalent to finding it in the table.
        can you please elaborate ?

        thanks,
        yg
        --
        http://ygdes.com / http://yasep.org
      Your message has been successfully submitted and would be delivered to recipients shortly.