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Re: Lucas-Jacobi identity

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  • mistermac39
    One question that David could answer under water. But, first, the background. When he made his observation a week or so ago re Sophie G primes, he found a
    Message 1 of 2 , Oct 23, 2002
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      One question that David could answer under water.

      But, first, the background.

      When he made his observation a week or so ago re Sophie G primes, he
      found a certain form of them that had not been covered on Blair
      Kelly's site.

      I then took up interest in the Lucas series called, I believe, Pell
      which goes 1,2,5,12....

      For the simple reason that SG goes n,2n+1 in a similar way.

      I think, without being dogmatic (ie sure,certain) about it, that all
      the other SGs are in this Pell series, or its friend Pucas
      1,3,7,17..., which plays the "lucas" to pell's "fibonacci" by the
      relation
      Pell(2n)=2*Pell(n)*Pucas(n).

      (2p+1)|Pucas(p) except for David's SGs, I conjecture, which, if true
      makes Phil Carmody's intuition, if not the execution,correct (the
      iff) of Phil's "raise" in David's first post.

      My question is whether Jacobi and his Lucas identities might also
      hold in part for Pell-Pucas series. I hope someone will think of a
      better name than Pucas, but its very inappropriateness makes it a
      point to drive home what I am getting at.

      Are there any other Lucas-Fibonacci Pucas-pell pairs is another
      question for David, or any other Lucas expert.

      John
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