## puzzle

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• 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
• 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,...
• 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/
>
>
>
>
• 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/
> >
> >
> >
> >
>
• 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
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/
>> >
>> >
>> >
>> >
>>
>
>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
>
• ... 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/
>>
>>
>>
>>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
>
>
>
• ... 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.
but since I had my ggf() at hand, I found the other before.

Maximilian
• 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]
• 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]
• ... 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
>
> 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. :)
• 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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