Problem 396

[OskarS]

I saw that a previous thread on this problem had been locked, but I actually need something about this problem clarified, so I figured I'd start a new thread. If this is inappropriate, I apologize, and feel free to delete or lock this one too.

I keep getting an off-by-one error when calculating the length of the sequence and comparing it to the examples in the problem description. For instance, for G(2) the page says that the length is 3, but the way I calculate it, the sequence is {2,2,1,0}, with a length of 4. Similarly, I get 22 for G(4) and 382 for G(6).

This would be simple enough to correct (just subtract 1!), but I'm concerned that I might not be getting some part of the problem. Does the final 0 not count in the sequence, so that the sequence for G(2) is {2,2,1}, not {2,2,1,0}? That would be the most obvious answer, I guess. I have some ideas about how to solve it, but I really would like this clarified first.

Thanks!

[Marcus_Andrews]

From the problem statement:

Let G(n) be the number of nonzero elements in the nth weak Goodstein sequence.

In other words, the list underlying G(2) would be {2, 2, 1}.

[OskarS]

Ahh, I see. I don't know how I missed that. Thanks!

[kenbrooker]

Problem reads:

It can also be verified that SumG(n) = 2517 for 1 <= n <= 8.

I think intended is:

It can also be verified that SumG(n) = 2517 for 1 <= n <= 7.

How I wished that the implied
G(8) was as simple as zero.

[v6ph1]

Read carefully:

It can also be verified that SumG(n) = 2517 for 1 <= n < 8.

The second one is just a less not a less-equal

[kenbrooker]

Sorry and Thanks Much...

When I copy and paste <= into my Java programs they are changed to < and
I have to correct them to <= and
I over-corrected!