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Re: [PrimeNumbers] puzzle

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  • Jack Brennen
    ... It looks like it s just the quadratic 3*x^2-20*x+74.
    Message 1 of 24 , Dec 9, 2011
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      > ? vector(9,x,3*x^2-20*x+74)
      > [57, 46, 41, 42, 49, 62, 81, 106, 137]

      It looks like it's just the quadratic 3*x^2-20*x+74.


      On 12/9/2011 8:40 AM, Maximilian Hasler wrote:
      > It has g.f. (74 x^2 - 125 x + 57)/(x - 1)^3
      > and goes on:
      > 57, 46, 41, 42, 49, 62, 81, 106, 137, 174, 217, 266, 321, 382, 449,
      > 522, 601, 686, 777, 874, 977, 1086, 1201, 1322, 1449, 1582, 1721,
      > 1866, 2017, 2174, 2337, 2506, 2681, 2862, 3049, 3242, 3441, 3646,
      > 3857, 4074, 4297, 4526, 4761, 5002, 5249, 5502, 5761, 6026, 6297,
      > 6574, 6857, 7146, 7441, 7742, 8049, 8362, 8681, 9006, 9337, 9674,
      > 10017, 10366, 10721, 11082, 11449, 11822, 12201, 12586, 12977, 13374,
      > 13777, 14186, 14601, 15022, 15449, 15882, 16321, 16766, 17217, 17674,
      > 18137, 18606, 19081, 19562, 20049, 20542, 21041,
      >
      > Maximilian
      >
      >
      >
      > On Fri, Dec 9, 2011 at 12:16 PM, ajo<sopadeajo2001@...> wrote:
      >> What is this sequence ?
      >>
      >> 57,46,41,42,49,62,81,106,137,...
      >>
      >>
      >>
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      >
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    • Maximilian Hasler
      ... I agree - the two sequences coincide. And I admit that the quadratic is a simpler description, but since I had my ggf() at hand, I found the other before.
      Message 2 of 24 , Dec 9, 2011
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        On Fri, Dec 9, 2011 at 12:56 PM, Jack Brennen <jfb@...> wrote:
        >
        >> ? vector(9,x,3*x^2-20*x+74)
        >> [57, 46, 41, 42, 49, 62, 81, 106, 137]
        >
        >
        > It looks like it's just the quadratic 3*x^2-20*x+74.

        I agree - the two sequences coincide.
        And I admit that the quadratic is a simpler description,
        but since I had my ggf() at hand, I found the other before.

        Maximilian
      • Robin Garcia
        The values you give seem to be correct, but the polynomials wrong: ? for(x=2,20, print(f(x))) 103 87/2 247/9 641/32 1971/125 13 3793/343 2463/256 2069/243
        Message 3 of 24 , Dec 9, 2011
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          The values you give seem to be correct, but the polynomials wrong:

          ? for(x=2,20, print(f(x)))
          103
          87/2
          247/9
          641/32
          1971/125
          13
          3793/343
          2463/256
          2069/243
          1909/250
          9213/1331
          1823/288
          12811/2197
          1854/343
          1889/375
          9659/2048
          21783/4913
          2033/486
          27157/6859

          [Non-text portions of this message have been removed]
        • Robin Garcia
          Ok, but now can anybody tell where the idea came from ,or in other words, what do these numbers originally pretend to represent ? [Non-text portions of this
          Message 4 of 24 , Dec 9, 2011
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            Ok, but now can anybody tell where the idea came from ,or in other words, what do these numbers originally pretend to represent ?

            [Non-text portions of this message have been removed]
          • Mark
            ... The worst case scenario is that the original number sequence came from someone s high school homework assignment. :)
            Message 5 of 24 , Dec 9, 2011
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              --- In primenumbers@yahoogroups.com, Robin Garcia <sopadeajo2001@...> wrote:
              >
              > Ok, but now can anybody tell where the idea came from ,or in other words, what do these numbers originally pretend to represent ?
              >
              > [Non-text portions of this message have been removed]
              >

              The worst case scenario is that the original number sequence came from someone's high school homework assignment. :)
            • Robin Garcia
              The worst case scenario is that the original number sequence came from someone s high school homework assignment. :) Well, yes the level is not a high level.
              Message 6 of 24 , Dec 9, 2011
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                "The worst case scenario is that the original number sequence came from someone's high school homework assignment. :)"


                Well, yes the level is not a high level. What i mean is the polinomial fits  pretty well, but originally i was thinking 
                in a base b and numbers  b^2+(b-2^2)^2+(b-3^2)^2.  Nothing very hard, but for b=10 you get 10^2+6^2+1^2=137,
                which obsesses so much David.  It was just fun for me.

                [Non-text portions of this message have been removed]
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