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OT: squarefree sequence

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  • jbrennen <jack@brennen.net>
    Just a bit off-topic, but combining the squarefree concept with sequences of the form k*2^n+1, I found this factoid: 70785*2^n+1 is squarefree for 0
    Message 1 of 1 , Dec 31, 2002
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      Just a bit off-topic, but combining the squarefree concept with
      sequences of the form k*2^n+1, I found this factoid:

      70785*2^n+1 is squarefree for 0 <= n <= 153.

      Note that any k with such a long sequence of squarefree numbers
      is also probably a good k for yielding primes; in order to be
      squarefree for such a long run, the members of the sequence must
      be free of small divisors.

      [Note: I tried to come back to the topic of prime numbers :) ]

      On the other side of the coin:

      27887*2^n+1 is non-squarefree for 0 <= n <= 4.

      Similarly, such values of k are probably not good k values for
      yielding primes.
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