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  • mcnamara_gio
    Define sequence a(n+1)=n*f(n)+a(n), a(1)=2, f(n) is nth term of fibonacci sequence. The first few terms are 2,3,7,13,25,73........... Notice that all terms
    Message 1 of 3 , Mar 4, 2005
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      Define sequence a(n+1)=n*f(n)+a(n), a(1)=2, f(n) is nth term of
      fibonacci sequence. The first few terms are 2,3,7,13,25,73...........
      Notice that all terms except 25 are primes. I think that other terms
      of the sequence are even so I think there will be no more primes. What
      do you think?
    • Décio Luiz Gazzoni Filho
      ... There seems to be a definite pattern to the parity of n*f(n). Try to work from there and see what you can prove about your sequence. Décio [Non-text
      Message 2 of 3 , Mar 4, 2005
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        On Friday 04 March 2005 15:33, you wrote:
        > Define sequence a(n+1)=n*f(n)+a(n), a(1)=2, f(n) is nth term of
        > fibonacci sequence. The first few terms are 2,3,7,13,25,73...........
        > Notice that all terms except 25 are primes. I think that other terms
        > of the sequence are even so I think there will be no more primes. What
        > do you think?

        There seems to be a definite pattern to the parity of n*f(n). Try to work from
        there and see what you can prove about your sequence.

        Décio


        [Non-text portions of this message have been removed]
      • Trey G
        For... f( 1): 1 f( 2): 1 f( 3): 2 f( 4): 3 f( 5): 5 f( 6): 8 f( 7): 13 f( 8): 21 f( 9): 34 f(10): 55 I get... a( 1): 2 a( 2): 3 a( 3): 5 a( 4): 11 a( 5): 23 a(
        Message 3 of 3 , Mar 5, 2005
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          For...

          f( 1): 1
          f( 2): 1
          f( 3): 2
          f( 4): 3
          f( 5): 5
          f( 6): 8
          f( 7): 13
          f( 8): 21
          f( 9): 34
          f(10): 55

          I get...

          a( 1): 2
          a( 2): 3
          a( 3): 5
          a( 4): 11
          a( 5): 23
          a( 6): 48
          a( 7): 96
          a( 8): 187
          a( 9): 355
          a(10): 661

          .....

          --- mcnamara_gio <mcnamara_gio@...> wrote:
          >
          > Define sequence a(n+1)=n*f(n)+a(n), a(1)=2, f(n) is
          > nth term of
          > fibonacci sequence. The first few terms are
          > 2,3,7,13,25,73...........
          > Notice that all terms except 25 are primes. I think
          > that other terms
          > of the sequence are even so I think there will be no
          > more primes. What
          > do you think?
          >
          >
          >
          >




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