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Re: [PrimeNumbers] puzzle

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  • Maximilian Hasler
    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,
    Message 1 of 24 , Dec 9, 2011
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      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/
      >
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      >
      >
      >
    • Mark
      I haven t comprehended Maximilian s result but 3x^2 - 14x + 57 works. Mark
      Message 2 of 24 , Dec 9, 2011
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        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,...
        > >
        > >
        > >
        > > ------------------------------------
        > >
        > > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
        > > The Prime Pages : http://www.primepages.org/
        > >
        > > Yahoo! Groups Links
        > >
        > >
        > >
        >
      • 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 3 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,...
          >> >
          >> >
          >> >
          >> > ------------------------------------
          >> >
          >> > 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
          >
          >
          >
        • Jack Brennen
          ... It looks like it s just the quadratic 3*x^2-20*x+74.
          Message 4 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 5 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 6 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 7 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 8 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 9 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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