strict partitions into catalans and powers of 3

[Roland Bacher]

such that 0< S-P_S(1/4)-Q_S(1/3)<min(1/4^(A+1),1/3^(B+1)).
since a very huge first counterexample can the be written as
  
 
Return-Path: <reismann at free.fr>
X-Ids: 165
Message-ID: <1170087804.45be1f7cb0d0f at imp.free.fr>
Date: Mon, 29 Jan 2007 17:23:24 +0100
From: reismann at free.fr
To: seqfan at ext.jussieu.fr
Subject: Re: New seq : primes of level (1,12..16)
References: <200701271408.JAA02756 at fry.research.att.com> <1169912141.45bb714d2206c at imp.free.fr>
In-Reply-To: <1169912141.45bb714d2206c at imp.free.fr>
MIME-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 8bit
User-Agent: Internet Messaging Program (IMP) 3.2.5
X-Originating-IP: 82.67.203.177
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-2.0.2 (shiva.jussieu.fr [134.157.0.165]); Mon, 29 Jan 2007 17:24:06 +0100 (CET)
X-Virus-Scanned: ClamAV 0.88.5/2500/Mon Jan 29 10:43:16 2007 on shiva.jussieu.fr
X-Virus-Status: Clean
X-Miltered: at shiva.jussieu.fr with ID 45BE1F80.003 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)!

Dear seqfans,

The new graph of (ln(weight),ln(level)) with the twin primes ((A001359 - (3))
and the levels 1 (A006562 + A117876 + A118464...). These two sets form the
limits of the classification :
http://reismann.free.fr/classement.php

level(1,15) :
264426203,295902073,361949821,704544167
level(1,16) :
356604959,613768081,709208323,950803363,979872743
level(1,17) :
364058659

More values are welcome.

Best,
Rémi

Selon reismann at free.fr:

> Dear seqfan,
>
> I submitted five sequences about the primes of level(1,i), levels(1,12 to
> 16).
> Def : Let p(i) denote the i-th prime. If 2 p(n) - p(n+1) (or p(n) - g(n)) is
> a
> prime, say p(n-i), then we say that p(n) has level(1,i), with g(n) = p(n+1) -
> p(n).
>
> p(50000000)= 982451653.
> On the first 50 million primes, I found only on level (1,17) :
> prime(19517159)=364058659
>
> prime(19517160)-prime(19517159)=prime(19517159)-prime(19517159-17),
> prime(19517160)-prime(19517159)=prime(19517159)-prime(19517142),
> 364058839 - 364058659 = 364058659 - 364058479=180=6*30,
> prime(19517159) has a level 1 in A117563,
> prime(19517159)= 364058659 has a level(1,17).
>
> More values are welcome.
>
> Best,
>
> Rémi
>
>





Dear Funsters and SeqFans,  This is neither fun nor to do
with sequences, I'm afraid.  But a friend of a friend
has been talking to me about making a 3-D model
of the trochea and lungs, modeling the flow of air.
This sounds like classical numerical analysis,
and I know there are experts on this list.
Does anyone know of previous work on this problem,
or on similar problems?

If so please write to me off-line.  Thanks!
Neil (njas at research.att.com)