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Re: [PrimeNumbers] Re: puzzle

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  • Maximilian Hasler
    Oops, sorry, there was an error of sign in the denominator. It should be gf = (74 x^2 - 125 x + 57)/(1 - x)^3 = 57 + 46*x + 41*x^2 + 42*x^3 + 49*x^4 + 62*x^5 +
    Message 1 of 24 , Dec 9, 2011
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      Oops, sorry, there was an error of sign in the denominator.
      It should be
      gf = (74 x^2 - 125 x + 57)/(1 - x)^3
      = 57 + 46*x + 41*x^2 + 42*x^3 + 49*x^4 + 62*x^5 + 81*x^6 + 106*x^7
      + 137*x^8 + 174*x^9 + 217*x^10 + 266*x^11 + 321*x^12 + 382*x^13
      + 449*x^14 + 522*x^15 + 601*x^16 + 686*x^17 + 777*x^18 + O(x^19)

      Maximilian



      On Fri, Dec 9, 2011 at 12:45 PM, Mark <mark.underwood@...> wrote:
      >
      > I haven't comprehended Maximilian's result but
      > 3x^2 - 14x + 57
      > works.
      >
      > Mark
      >
      >
      > --- In primenumbers@yahoogroups.com, Maximilian Hasler <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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      >> > The Prime Pages : http://www.primepages.org/
      >> >
      >> > Yahoo! Groups Links
      >> >
      >> >
      >> >
      >>
      >
      >
      >
      >
      > ------------------------------------
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      >
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    • Jack Brennen
      ... It looks like it s just the quadratic 3*x^2-20*x+74.
      Message 2 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,...
        >>
        >>
        >>
        >> ------------------------------------
        >>
        >> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
        >> The Prime Pages : http://www.primepages.org/
        >>
        >> Yahoo! Groups Links
        >>
        >>
        >>
        >
        >
        > ------------------------------------
        >
        > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
        > The Prime Pages : http://www.primepages.org/
        >
        > Yahoo! Groups Links
        >
        >
        >
        >
        >
      • 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 3 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 4 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 5 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 6 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 7 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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