--- On Tue, 6/19/12, Maximilian Hasler <

maximilian.hasler@...> wrote:

> b) if not, what's the maximum length, and why? What V_0 leads to the

> > smallest final prime?

> the maximum length is 4, as you can see when you look at the

> sequence V_i

> mod 3:

> 1,1,1 => 1,1,0

> 2,2,2 => 2,2,0

> 1,1,2 => 1,2,1

> 1,2,1 => 2,1,1

> 2,1,1 => 1,1,1

> 1,2,2 => 2,2,2

> 2,1,2 => 1,2,2

> 2,2,1 => 2,1,2

You're permitted to start with 3s, so that can be extended by 2.

0,1,1 => 1,1,2

0,0,1 => 0,1,1

> what is the "final prime" ?

> (2,2,2) leads to (2,2,6), so the final prime is 2 ?

(2,2,6) doesn't exist, so (2,2,2) doesn't lead there.

In the <3,3,5> example I gave, 19 is the final prime, as no other primes were added after it.

> > 2) As above, but with n=5

> > 3) As above, but with n=7

> > 4) Generalise, what do you predict for other n?

> >

> It seems that in these cases the maximum length is always

> 5. But I may be wrong...

So you don't think the 5-tuplet

[5, 83, 3, 7, 3]

would be extended in turn 8 times by the primes

[101, 197, 311, 619, 1231, 2459, 4817, 9437]

(and no, that's not the answer, merely illustrative)?

It seems you've made some assumptions that have stopped you from investigating every possibility.

Phil