Re: Fun, weird, sad, cool

From: The Last Danish Pastry (clivet_at_gmail.com)
Date: 09/10/04 

Date: Fri, 10 Sep 2004 15:09:06 +0100

"James Harris" <jstevh@msn.com> wrote in message
news:3c65f87.0409091836.56fa26d1@posting.google.com...

> After showing the actual linkages from my work to stuff like
> Legendre's Formula I had a sad fear that maybe, you know, like maybe
> mathematicians never understood the recurrence relationship with the
> phi function.
>
> After all, my dS(x,y) function is rather specifically the count of
> composites up to and including x that have y as a factor that do not
> have any prime less than y as a factor.
>
> And I showed how it connects to a difference between phi sieve
> functions, so if mathematicians had understood that the difference had
> some interesting features, wouldn't they have talked about it?
>
> Like that definition I gave above for dS(x,y) means that if y is not
> prime then dS(x,y) = 0, which is why my prime counting function finds
> primes on its own.
>
> And then it gets weirder as I gave the derivation, finally, for
>
> [N/p] - [N/2p] - 1 = [(N-p)/2p]
>
> with p an odd prime, where in general you have
>
> [N/k] - [N/2k] - 1 = [(N-k)/2k]
>
> with k a natural greater than 1.
>
> Such a simple relation methinks can't be new. I wonder...

Back in the mists of time... well... six weeks ago...
No Way was explaining something to you...
http://tinylink.com/?2GoRBD5hlN

No Way:
"Yes, it's constantly combing two terms with:
[(N+k)/(2*k)] = [N/k] - [N/(2*k)]"

Harris:
"How do you get that?"

Harris:
"I'd be interested in a proof of that relation.

Note that for the relations I gave I proved [(N-4)/6] directly by the
method I've posted, and then used it with my prime counting function
to find the other formulas.

So, not surprisingly, I'm curious about how you came up with your
formula, as I doubt you used my prime counting function.

That is, I'd like to see the proof of your formula:

[(N+k)/(2*k)] = [N/k] - [N/(2*k)]"

A couple of people pointed out that the proof was trivial.

Now, if we take No Way's formula and replace N by N-k we get...

[N/(2*k)] = [N/k] - 1 - [(N-k)/(2*k)]

which... good grief... is your formula!!

Evidently No Way has used time travel to steal your formula and has then
replaced N by N+k in order to try to cover his tracks. That is the only
explanation. 

-- 
Clive Tooth
http://www.clivetooth.dk

Relevant Pages

  • Re: Partial difference equation, primes
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  • JSH: Forget everything, I Quit for good
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  • Re: Partial difference equation, primes
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  • Re: Partial difference equation, primes
    ... > The compressed explicit prime counting function exists as I've shown. ... What does mean "having less computational complexity"? ... > The reality is that I'm far ahead of mathematicians at every level, ... >> I agree on the fact you are not a sheep. ...
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