Is A073071 correct?

Thu May 1 12:02:29 CEST 2008

seq(A000001(n),n=1..80) ;
Return-Path: <mlb at well.com>
X-Ids: 168
X-WELL-Auth: Yes
Message-Id: <200805011626.m41GQ6RM027612 at smtp.well.com>
X-Mailer: QUALCOMM Windows Eudora Version 7.1.0.9
Date: Thu, 01 May 2008 09:26:07 -0700
To: =?iso-8859-1?Q?=22Beno=EEt_Jubin=22?= <benoit.jubin at gmail.com>,
   seqfan at ext.jussieu.fr
From: Marc LeBrun <mlb at well.com>
Subject: Re: A137316 (group automorphisms)
In-Reply-To: <79b0f44e0804292043w55a0a0f1r5c5ad39007a215 at mail.gmail.com>
References: <79b0f44e0804292043w55a0a0f1r5c5ad39007a215 at mail.gmail.com>
Mime-Version: 1.0
Content-Type: text/plain; charset="iso-8859-1"; format=flowed
X-Virus-Scanned: ClamAV 0.92/7007/Thu May  1 17:34:23 2008 on shiva.jussieu.fr
X-Virus-Scanned: ClamAV version 0.93, clamav-milter version 0.93 on wodehouse.well.com
X-Virus-Status: Clean
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.168]); Thu, 01 May 2008 18:26:10 +0200 (CEST)
X-Miltered: at jchkmail.jussieu.fr with ID 4819EF1F.001 by Joe's j-chkmail (http : // j-chkmail dot ensmp dot fr)!
X-j-chkmail-Enveloppe: 4819EF1F.001/208.17.81.207/smtp.well.com/smtp.well.com/<mlb at well.com>
X-j-chkmail-Score: MSGID : 4819EF1F.001 on jchkmail.jussieu.fr : j-chkmail score : X : R=. U=. O=. B=0.273 -> S=0.273
X-j-chkmail-Status: Unsure
Content-Transfer-Encoding: 8bit
X-MIME-Autoconverted: from quoted-printable to 8bit by idf.ext.jussieu.fr id m41GQA2M088624
 >=Benoît Jubin
 > As far as I know, there is no sequence yet giving the number of
 > automorphisms of the dicyclic (or binary dihedral) group of order 4n,
 > and its subsequence consisting of indices a power of 2, corresponding
 > to the generalized quaternion groups. Do you think they are worth
 > adding ?
 > Also, do you think it is worth doing the same thing with the numbers
 > of endomorphisms, inner/outer automorphisms, (normal) subgroups ?
Return-Path: <zakseidov at yahoo.com>
X-Ids: 168
DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws;
  s=s1024; d=yahoo.com;
  h=X-YMail-OSG:Received:Date:From:Subject:To:Cc:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID;
  b=W+UiP9PWrJb4Z1ko/U9S1IAZT58Fn5ZOysZAVqhpnibWX9CePHFZc0AuNe01UwmF2RhDxNHCDyh8MxxRtWfRTCSf08kVJpAc1LLOAW9MxuJ8KQ+TPi80/lqJKac97F43sNatPQ81gR1A2Egvwh9SaoT+Uu1qmfuQGDo/8b3r778=;
X-YMail-OSG: 8gy9VG8VM1k1IwBxg_gwWwi4db8FMLlufAZnCF7SY0uAWj1YCtf.wSgcxJN6nMUUAQJDnusONX8mOiXKzK0pf.VeKu_0QtL1Rs0BrdgfYwtOjbLwRSvhmRr_MuQ-
Date: Thu, 1 May 2008 09:27:32 -0700 (PDT)
From: zak seidov <zakseidov at yahoo.com>
Subject: Re: Is A073071 correct?
To: Richard Mathar <mathar at strw.leidenuniv.nl>, seqfan at ext.jussieu.fr
Cc: benoit7848c at orange.fr
In-Reply-To: <200805011427.m41ERfZg007777 at amer.strw.leidenuniv.nl>
MIME-Version: 1.0
Content-Type: text/plain; charset=iso-8859-1
Content-Transfer-Encoding: 8bit
Message-ID: <902059.45930.qm at web38208.mail.mud.yahoo.com>
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.168]); Thu, 01 May 2008 18:27:35 +0200 (CEST)
X-Virus-Scanned: ClamAV 0.92/7007/Thu May  1 17:34:23 2008 on shiva.jussieu.fr
X-Virus-Status: Clean
X-Miltered: at jchkmail.jussieu.fr with ID 4819EF76.008 by Joe's j-chkmail (http : // j-chkmail dot ensmp dot fr)!
X-j-chkmail-Enveloppe: 4819EF76.008/209.191.124.151/web38208.mail.mud.yahoo.com/web38208.mail.mud.yahoo.com/<zakseidov at yahoo.com>
X-j-chkmail-Score: MSGID : 4819EF76.008 on jchkmail.jussieu.fr : j-chkmail score : X : R=. U=. O=. B=0.214 -> S=0.214
X-j-chkmail-Status: Ham

Defn with k!! (not k!) gives:
3,4,6,8,10,12,14,16,19,21,23,25,28,30,32,34,37,39,41,43,46,48,50,52,55,57,59,62,64,66,68,71,73,75,78,80,82,84,87,89,91,94,96,98
- not exactly A073071 
zak

--- Richard Mathar <mathar at strw.leidenuniv.nl> wrote:

> 
> pp> From seqfan-owner at ext.jussieu.fr  Thu May  1
> 03:27:20 2008
> pp> Date: Thu, 01 May 2008 03:26:58 +0200
> pp> From: Peter Pein <petsie at dordos.net>
> pp> To: seqfan at ext.jussieu.fr
> pp> Subject: Is A073071 correct?
> pp> ...
> pp> propably I overlook something important, but I
> can't figure out what.
> pp> 
> pp> The definition of
> http://www.research.att.com/~njas/sequences/A073071
> is:
> pp> "Least k such that k! >
> prime(1)*prime(2)*...*prime(n) where prime(n) is the
> pp> n-th prime."
> pp> and it starts with n=1.
> pp> ....
> 
> njas> From seqfan-owner at ext.jussieu.fr  Thu May  1
> 15:29:27 2008
> njas> Date: Thu, 1 May 2008 09:29:03 -0400
> njas> From: "N. J. A. Sloane"
> <njas at research.att.com>
> njas> To: mathar at strw.leidenuniv.nl,
> seqfan at ext.jussieu.fr
> njas> Subject: Re: Is A073071 correct?
> njas> Cc: benoit7848c at orange.fr,
> njas at research.att.com
> njas> Another possibility is that the sequence
> originally said:
> njas> 
> njas> Least k such that k! > P(1)*P(2)*...*P(n).
> njas> 
> njas> and I guessed that P(i) meant prime(i).  But
> maybe it meant
> njas> partitions(i) ?  Benoit, do you remember what
> njas>...
> 
> The interpretation P=partitions keeps the growth
> rate close to what
> we are searching for, but it does not (yet) fit the
> original
> A073071 version, I think. The two test cases are:
> 
> "Smallest k such that k! > A058694(n)", n>=1 :
>
2,3,4,5,6,7,8,10,11,13,14,16,18,19,21,23,25,26,28,30,32,34,36,38,40,42,44,47,49,51,53,55,58,60,
>
62,65,67,70,72,74,77,79,82,84,87,90,92,95,97,100,103,105,108,111,114,116,119,122,125,128,131,134,
>
136,139,142,145,148,151,154,157,160,163,166,169,172,176,179,182,185,188
> 
> "Smallest k such that k! >= A058694(n)", n>=1 ,
> differs in first 3 terms:
>
1,2,3,5,6,7,8,10,11,13,14,16,18,19,21,23,25,26,28,30,32,34,36,38,40,42,44,47,49,51,53,55,58,60,
>
62,65,67,70,72,74,77,79,82,84,87,90,92,95,97,100,103,105,108,111,114,116,119,122,125,128,131,134,
>
136,139,142,145,148,151,154,157,160,163,166,169,172,176,179,182,185,188
> 
> A000041 := proc(n)
>         combinat[numbpart](n) ;
> end:
> A058694 := proc(n)
>         local i ;
>         mul(A000041(i),i=1..n) ;
> end:
> 
> A000001 := proc(n)
>         for k from 1 do
> 		# optionally replace greater sign...
>                 if k! >  A058694(n) then
>                         RETURN(k) ;
>                 fi ;
>         od:
> end:
> 
> seq(A000001(n),n=1..80) ;
> 
> 


      ____________________________________________________________________________________
Be a better friend, newshound, and 
know-it-all with Yahoo! Mobile.  Try it now.  http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ