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  • ajo
    What is this sequence ? 57,46,41,42,49,62,81,106,137,...
    Message 1 of 24 , Dec 9, 2011
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      What is this sequence ?

      57,46,41,42,49,62,81,106,137,...
    • 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 2 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/
        >
        > Yahoo! Groups Links
        >
        >
        >
      • Mark
        I haven t comprehended Maximilian s result but 3x^2 - 14x + 57 works. Mark
        Message 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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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