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puzzle

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  • reney_nl
    A prime puzzle, I have 6 numbers: 1,2,3 22,25 and 1111 find a primeformula using these numbers (hint: divide 1111 into 2x11).. success! RJ
    Message 1 of 24 , Apr 4, 2005
      A prime puzzle,

      I have 6 numbers: 1,2,3 22,25 and 1111

      find a primeformula using these numbers (hint: divide 1111 into 2x11)..

      success!

      RJ
    • ajo
      What is this sequence ? 57,46,41,42,49,62,81,106,137,...
      Message 2 of 24 , Dec 9, 2011
        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 3 of 24 , Dec 9, 2011
          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 4 of 24 , Dec 9, 2011
            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 5 of 24 , Dec 9, 2011
              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 6 of 24 , Dec 9, 2011
                > ? 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 7 of 24 , Dec 9, 2011
                  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 8 of 24 , Dec 9, 2011
                    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 9 of 24 , Dec 9, 2011
                      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 10 of 24 , Dec 9, 2011
                        --- 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 11 of 24 , Dec 9, 2011
                          "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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