1)

a[1]=2

a[n_]:=a[n]=Ceiling[a[n-1]^(1+1/a[n-1])]

2)

a[1]=2;a[2]=3;

a[n_]:=a[n]=Ceiling[a[n-1]^(1+a[n-2]/a[n-1]^2)]

3)

a[1]=2;a[2]=3;

a[n_]:=a[n]=Ceiling[a[n-1]^(1-1/a[n-1]+2*a[n-2]/a[n-1]^2)]

In Mathematica functional form.

primenumbers@yahoogroups.com wrote:

>

--

>

>There are 3 messages in this issue.

>

>Topics in this digest:

>

> 1. RE Proof proposal, almost ready!

> From: Jose Ramón Brox <ambroxius@...>

> 2. I need to find an answer to my last posting.

> From: "chrisdarroch" <chrisdarr2@...>

> 3. Re: I need to find an answer to my last posting.

> From: mikeoakes2@...

>

>

>________________________________________________________________________

>________________________________________________________________________

>

>Message: 1

> Date: Sat, 23 Apr 2005 01:44:04 +0200

> From: Jose Ramón Brox <ambroxius@...>

>Subject: RE Proof proposal, almost ready!

>

>Only a little remainder of what was said in 07 April by "chrisdarroch":

>

>----- Original Message -----

>Sent: Thursday, April 07, 2005 9:38 AM

>Subject: [PrimeNumbers] Proof proposal, almost ready!

>

>My proof proposal is almost ready and I am pretty confident about it's

>rigour and solution.

>

>[...]

>

>So, for those interested, please bare with me on my proof proposal, I

>will be out for 8 days.

>

>[...]

>

>Chris

>

>------------------------------------

>

>There are passed 16 days already, twice the amount Chris needed. It's true that he has

>posted some questions here since then; but he has not shed a single light about his

>rigorous solution for the GC.

>

>I think his not going to post anyone. We have seen cases like his before in this list.

>Probably he will keep sending simple questions and eventually quit silently from the

>group. Im not sure, though.

>

>Jose Brox.

>

>

>

>

>

>

>

>

>

>________________________________________________________________________

>________________________________________________________________________

>

>Message: 2

> Date: Sat, 23 Apr 2005 00:28:07 -0000

> From: "chrisdarroch" <chrisdarr2@...>

>Subject: I need to find an answer to my last posting.

>

>

>

>If I can find an answer to the general case of my last postings then I

>can post my proof proposal immediately!

>

>I guess then, without that answered, my proof isn't ready.

>

>A few people seem to think that my question is trivial.

>

>Jens thought and practically stated that was the case.

>

>When I pushed him on the matter, he seemed to backpedal on that claim.

>

>My initial question included a confusing 'div' operator.

>

>>>Can I predict an A, at 105x div 31 ? Where x is a natural number?

>

>My subsequent attempt used n instead of A but the function was more

>mainstream in format. But it clearly asks whether I can predict an n.

>

>>>Can I predict an n, at column, integerpart(105x/31) ? Where x is an

>>>integer

>

>Jens seemed to take this question to mean, that given the data, could

>I somehow find an n; thus brute force, trial and error was allowable.

>

>Given this interpretation, he retorted that my question was trivial.

>

>Surely the term 'predict', indicates sufficiently that I want to

>disclude trial and error searching!

>

>This could have been a potentially damaging indictment of yet another

>in a series of trivial questions; as those who might have looked at it

>more closely (including the more important general case, posted soon

>after)my have accepted Jens' analysis.

>

>Jose is following on in this indictment re:

>

>>>Probably he will keep sending simple questions

>

>If you all think that this is a trivial question, then I challenge you

>to answer it!

>

>Chris

>

>

>

>

>

>

>

>

>

>

>

>

>________________________________________________________________________

>________________________________________________________________________

>

>Message: 3

> Date: Sat, 23 Apr 2005 04:09:57 -0400

> From: mikeoakes2@...

>Subject: Re: I need to find an answer to my last posting.

>

>"chrisdarroch" <chrisdarr2@...> writes:

>

>>If I can find an answer to the general case of my last postings

>>then I can post my proof proposal immediately!

>>

>>I guess then, without that answered, my proof isn't ready.

>>

>

>How can you possibly know whether or not you will have a "proof" if you don't yet know the answer to your question. That is absurd.

>

>Furthermore, you seem now to have resorted to blaming the (long-suffering) members of this group for the non-appearance of your "proof".

>

>Dear god, when will this thread end?

>(Moderators, are you listening?)

>

>-Mike Oakes

>

>

>

>________________________________________________________________________

>________________________________________________________________________

>

>

>Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

>The Prime Pages : http://www.primepages.org/

>

>

>------------------------------------------------------------------------

>Yahoo! Groups Links

>

>

>

>

>------------------------------------------------------------------------

>

>

>

>

>

Respectfully, Roger L. Bagula

rlbtftn@... , 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814

__________________________________________________________________

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