[seqfan] Re: A greedy sequence

[Maximilian Hasler]

I get different values after 8242614:

{r=1;u=[];l=1;for(n=1,99,while(setsearch(u,l),l++);m=ceil(1/r);while(setsearch(u,m),m++);print1(m",");r-=1/m;r|r=1;u=setunion(u,Set(m)))}

1,2,3,6,4,5,7,8,9,10,15,230,57960,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
1544,8242614,92401258430373,36895712779713620978746324067,
60304359897310876267718211889396254868127989558646609702375,
62695256782044591165065261300234082916628758813801442183166200537944992344643145754256231500695609206171283933420542000,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,202,60402,4574207768,21535327512365363703
...

Maximilian

On Sat, Feb 14, 2009 at 4:24 PM, Jeremy Gardiner
<jeremy.gardiner at btinternet.com> wrote:
>
> The following 'greedy' sequence is formed by summing unit fractions until
> the sum is 1, and repeating using up the 'left over' fractions:
>
> 1,
> 2,3,6,
> 4,5,7,8,9,10,15,230,57960,
> 11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1544,8242614,
> 31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,5
> 6,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81
> ,82,202,60402,
>
> (according to my BASIC program implementation: could be errors due to
> accuracy of representation)
>
> - anyone else find this interesting, or seen this before?
>
> Likely needs some more investigation before thinking about submitting to
> OEIS!
>
> Perhaps related to the The Greedy Algorithm for Unit Fractions:
> http://www.mathpages.com/home/kmath454.htm
>
> I guess it may not be known if all of the sub-sequences terminate?
>
> Jeremy
>
>
>
>
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