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## Re: Puzzle: Sphenic chain by factor concatenation

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• ... Congrats! I m now in the low 90s, but do not expect to make it to length 100. David
Message 1 of 16 , Jun 15, 2011
Kevin Acres <research@...> wrote:

> {sphen84a = [114,
> 3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 3, 6, 2, 2, 1, 1, 3, 4, 2, 6,
> 6, 4, 2, 6, 2, 2, 4, 4, 3, 2, 1, 3, 5, 6, 2, 4, 5, 5, 1, 4,
> 6, 4, 6, 4, 5, 1, 3, 1, 1, 1, 4, 1, 1, 4, 3, 4, 2, 3, 4, 2,
> 3, 2, 1, 5, 4, 5, 6, 3, 5, 6, 3, 5, 6, 6, 3, 4, 4, 2, 4, 4,
> 4, 3, 4];}
>
> {sphen84b = [114,
> 3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 3, 6, 2, 2, 1, 1, 3, 4, 2, 6,
> 6, 4, 2, 6, 2, 2, 4, 4, 3, 2, 1, 3, 5, 6, 2, 4, 5, 5, 1, 4,
> 6, 4, 6, 4, 5, 1, 3, 1, 1, 1, 4, 1, 1, 4, 3, 4, 2, 3, 4, 2,
> 3, 2, 1, 5, 4, 5, 6, 3, 5, 6, 3, 5, 6, 6, 3, 4, 4, 2, 4, 4,
> 4, 3, 3];}

Congrats!

I'm now in the low 90s, but do not expect to make it to length 100.

David
• ... In fact, I was able to reach length 105: {sphen105 = [114, 3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 1, 6, 1, 4, 1, 3, 2, 3, 2, 6, 1, 6, 3, 5, 5, 6, 2, 1, 6, 6, 6, 1,
Message 2 of 16 , Jun 15, 2011

> do not expect to make it to length 100

In fact, I was able to reach length 105:

{sphen105 = [114,
3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 1, 6, 1, 4, 1, 3, 2, 3, 2, 6,
1, 6, 3, 5, 5, 6, 2, 1, 6, 6, 6, 1, 2, 5, 4, 3, 5, 2, 5, 2,
4, 1, 5, 1, 6, 5, 3, 3, 5, 5, 2, 1, 5, 5, 1, 6, 4, 5, 5, 3,
5, 2, 4, 4, 4, 3, 4, 5, 6, 4, 6, 3, 6, 4, 2, 4, 5, 2, 6, 1,
1, 4, 6, 1, 6, 1, 2, 3, 2, 4, 6, 3, 3, 1, 6, 3, 3, 3, 1, 3,
1, 5, 3, 1];}

contains 8 helpers, obtained by ECM, and then the chain of
is generated in less than 4 minutes.

David
• ... The best I can do at present is length 108: {sphen108 = [114, 3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 1, 6, 1, 4, 1, 3, 2, 3, 2, 6, 1, 6, 3, 5, 5, 6, 2, 1, 6, 6, 6,
Message 3 of 16 , Jun 16, 2011

> able to reach length 105

The best I can do at present is length 108:

{sphen108 = [114,
3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 1, 6, 1, 4, 1, 3, 2, 3, 2, 6,
1, 6, 3, 5, 5, 6, 2, 1, 6, 6, 6, 1, 2, 5, 4, 3, 5, 2, 5, 2,
4, 1, 5, 1, 6, 5, 3, 3, 5, 5, 2, 1, 5, 5, 1, 6, 4, 5, 5, 3,
5, 2, 4, 4, 4, 3, 4, 5, 6, 4, 6, 3, 6, 4, 2, 4, 5, 2, 6, 1,
1, 4, 6, 1, 6, 1, 2, 3, 2, 4, 6, 3, 3, 1, 6, 3, 3, 3, 1, 3,
5, 1, 4, 5, 2, 5, 2];}

with input and output in

David
• ... Length 109 is achieved by {sphen109 = [114, 3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 1, 6, 1, 4, 1, 3, 2, 3, 2, 6, 1, 6, 3, 5, 5, 6, 2, 1, 6, 6, 6, 1, 2, 5, 4, 3, 5,
Message 4 of 16 , Jun 20, 2011

> The best I can do at present is length 108

Length 109 is achieved by

{sphen109 = [114,
3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 1, 6, 1, 4, 1, 3, 2, 3, 2, 6,
1, 6, 3, 5, 5, 6, 2, 1, 6, 6, 6, 1, 2, 5, 4, 3, 5, 2, 5, 2,
4, 1, 5, 1, 6, 5, 3, 3, 5, 5, 2, 1, 5, 5, 1, 6, 4, 5, 5, 3,
5, 2, 4, 4, 4, 3, 4, 5, 6, 4, 6, 5, 6, 2, 1, 1, 6, 6, 5, 6,
6, 4, 6, 6, 2, 4, 4, 6, 6, 2, 5, 3, 1, 2, 2, 1, 2, 2, 4, 3,
1, 4, 3, 1, 2, 5, 3, 5];}

with input and output in

David
• Hi David, ... Well done for that. Its been windy here and wind = power outage where I live :-) One day I ll get a decent size UPS. Best Regards, Kevin.
Message 5 of 16 , Jun 20, 2011
Hi David,

At 02:20 PM 21/06/2011, djbroadhurst wrote:

>
> > The best I can do at present is length 108
>
>Length 109 is achieved by
>
> {sphen109 = [114,
> 3, 6, 6, 3, 2, 2, 4, 4, 3, 4, 1, 6, 1, 4, 1, 3, 2, 3, 2, 6,
> 1, 6, 3, 5, 5, 6, 2, 1, 6, 6, 6, 1, 2, 5, 4, 3, 5, 2, 5, 2,
> 4, 1, 5, 1, 6, 5, 3, 3, 5, 5, 2, 1, 5, 5, 1, 6, 4, 5, 5, 3,
> 5, 2, 4, 4, 4, 3, 4, 5, 6, 4, 6, 5, 6, 2, 1, 1, 6, 6, 5, 6,
> 6, 4, 6, 6, 2, 4, 4, 6, 6, 2, 5, 3, 1, 2, 2, 1, 2, 2, 4, 3,
> 1, 4, 3, 1, 2, 5, 3, 5];}

Well done for that. Its been windy here and "wind = power outage"
where I live :-)

One day I'll get a decent size UPS.

Best Regards,

Kevin.
• ... The current record is length 112, achieved by {sphen112a = [114, 3, 6, 6, 3, 2, 2, 1, 3, 3, 2, 2, 1, 5, 2, 3, 2, 1, 6, 4, 4, 2, 4, 4, 2, 5, 4, 2, 3, 4, 2,
Message 6 of 16 , Jun 23, 2011
Kevin Acres <research@...> wrote:

> > {sphen109 = [114,
....
> Well done for that. Its been windy here and "wind = power outage"
> where I live :-)

The current record is length 112, achieved by

{sphen112a = [114,
3, 6, 6, 3, 2, 2, 1, 3, 3, 2, 2, 1, 5, 2, 3, 2, 1, 6, 4, 4,
2, 4, 4, 2, 5, 4, 2, 3, 4, 2, 1, 3, 3, 6, 5, 4, 3, 1, 5, 4,
2, 5, 1, 1, 3, 4, 5, 5, 5, 5, 6, 3, 6, 1, 6, 1, 4, 3, 1, 6,
4, 6, 3, 1, 3, 2, 1, 2, 2, 6, 3, 2, 3, 5, 4, 6, 6, 5, 2, 2,
2, 3, 4, 6, 5, 2, 3, 3, 2, 6, 5, 1, 2, 6, 1, 4, 3, 5, 3, 3,
3, 4, 1, 4, 2, 2, 1, 2, 6, 3, 2];}

{sphen112b = [114,
3, 6, 6, 3, 2, 2, 1, 3, 3, 2, 2, 1, 5, 2, 3, 2, 1, 6, 4, 4,
2, 4, 4, 2, 5, 4, 2, 3, 4, 2, 1, 3, 3, 6, 5, 4, 3, 1, 5, 4,
2, 5, 1, 1, 3, 4, 5, 5, 5, 5, 6, 3, 6, 1, 6, 1, 4, 3, 1, 6,
4, 6, 3, 1, 3, 2, 1, 2, 2, 6, 3, 2, 3, 5, 4, 6, 6, 5, 2, 2,
2, 3, 4, 6, 5, 2, 3, 3, 2, 6, 5, 1, 2, 6, 1, 4, 3, 2, 3, 3,
4, 2, 2, 3, 2, 2, 1, 4, 5, 1, 1];}

with input and output in