OEIS on vacation!

Mon Jun 18 22:02:13 CEST 2007

starting now, for the next several weeks, the OEIS will 
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Date: Mon, 18 Jun 2007 20:59:18 -0400
From: "Maximilian Hasler" <maximilian.hasler at gmail.com>
To: "Sequence Fans" <seqfan at ext.jussieu.fr>
Subject: tabl vs tabf
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I just ran across the following:

A001265 Table T(n,k) in which n-th row lists prime factors of 2^n - 1
(n >= 2), with repetition.
KEYWORD nonn,tabl

A046051 Number of prime factors of Mersenne number M(n) = 2^n - 1
(counted with multiplicity).
COMMENT Length of row n of A001265.

IMHO, the former should be tabf, since it makes not much sense to
display it as triangle or so (even if in the present case this is
still "almost nice")

Unfortunately, the "tabf" kwhas no link associated to it.
What do you think about the possibility of "directly" associating to
the tabf kw the sequence of row lenths ? like, e.g., tabf(A046051) or
so ?

In these times of vacation, I don't dare to suggest to have an
automatic link to a small script that takes the second sequence to
format the first adequately.

I'd volunteer to write some PHP lines in order that e.g.

http://www.research.att.com/~njas/sequences/table?a=1265&tabf=46051

would do that.
(btw, is there some documentation about possible parameters to
http://www.research.att.com/~njas/sequences/table ?)

something like

if( @$_GET['tabf']) {
  $rowl = sequence_to_array( $_GET['tabf'] );
  $data = sequence_to_array( $_GET['a'] );
 print( "<h2> Sequence A$_GET[a] formatted using TABF(A$_GET[tabf])</h2>
<table>" );
while ($rowl and $data ){
  echo "\n <tr>";
  for(i=array_shift($rowl ), i>0 and $data, i--) echo "<td>",
array_shift($data) ;
}
echo "</table>";
}

That would already be sufficient !
(well, of course i'd add some additional gadgets & safety checks...)

M.H.

--Apple-Mail-1--101249128

This is related to something we've discussed before. The Quet  
Transform (see http://www.research.att.com/~njas/sequences/A101387)  
was also defined using a mapping from {permutations of the positive  
integers} to {sequences of positive integers with infinitely many  
ones}. I called this map T. Its relationship to the trace is t_p = T 
(p^-1). The Quet transform maps T(p) to T(p^-1).

On Jun 17, 2007, at 7:56 AM, Kimberling, Clark wrote:

> Dear Seqfans -
>
> Suppose p is a permutation of the positive integers, N.  If we  
> subtract 1 from every term and then delete 0, what's left is  
> another perm.  Iterate, and we get many perms.
>
> Now, let t(k) be the position of 1 in the kth iterate.
>
> Example:  p = (1,3,2,5,7,4,9,11,6,13,15,8,...) = A006369 (related  
> to 3X+1 problem)
> This choice of p yields trace sequence t =  
> (1,2,1,3,1,4,1,5,1,6,1,7,...) = A057979 essentially.
>
> A sequence t of positive integers is the trace of a perm if and  
> only if t has infinitely many 1's.  Let T be the set of all such t.
>
> Suppose t_p and t_q are traces of perms p and q.  Can someone find  
> a decent formula for t_r, where r is the composite perm p-of-q?
>
> I'd like to see such a formula - it would define a group operation  
> on the set T.
>
> Clark Kimberling

--Apple-Mail-1--101249128

<HTML><BODY style=3D"word-wrap: break-word; -khtml-nbsp-mode: space; -khtml=
m/~njas/sequences/A101387">http://www.research.att.com/~njas/sequences/A101=
387</A>) was also defined using a mapping from {permutations of the positiv=
e integers} to {sequences of positive integers with infinitely many ones}. =
I called this map T. Its relationship to the trace is t_p =3D T(p^-1). The =
Quet transform maps T(p) to T(p^-1).<DIV><BR><DIV><DIV>On Jun 17, 2007, at =
7:56 AM, Kimberling, Clark wrote:</DIV><BR class=3D"Apple-interchange-newli=
ne"><BLOCKQUOTE type=3D"cite">  <DIV><FONT face=3D"Arial" size=3D"2"><SPAN =
class=3D"305084614-17062007">Dear Seqfans -</SPAN></FONT></DIV> <DIV><FONT =
face=3D"Arial" size=3D"2"><SPAN class=3D"305084614-17062007"></SPAN></FONT>=
=A0</DIV> <DIV><FONT face=3D"Arial" size=3D"2"><SPAN class=3D"305084614-170=
62007">Suppose p is a permutation of the positive integers, N.=A0 If we sub=
tract 1 from every term and then delete 0, what's left is another perm.=A0 =
Iterate, and we get many perms.</SPAN></FONT></DIV> <DIV><FONT face=3D"Aria=
l" size=3D"2"><SPAN class=3D"305084614-17062007"></SPAN></FONT>=A0</DIV> <D=
IV><FONT face=3D"Arial" size=3D"2"><SPAN class=3D"305084614-17062007">Now, =
let t(k) be the position of 1 in the kth iterate.</SPAN></FONT></DIV> <DIV>=
<FONT face=3D"Arial" size=3D"2"><SPAN class=3D"305084614-17062007"></SPAN><=
/FONT>=A0</DIV> <DIV><FONT face=3D"Arial" size=3D"2"><SPAN class=3D"3050846=
14-17062007">Example:=A0 p =3D (1,3,2,5,7,4,9,11,6,13,15,8,...) =3D A006369=
ze=3D"2"><SPAN class=3D"305084614-17062007">This choice of p yields trace s=
equence t =3D (1,2,1,3,1,4,1,5,1,6,1,7,...) =3D A057979 essentially.</SPAN>=
</FONT></DIV> <DIV><FONT face=3D"Arial" size=3D"2"><SPAN class=3D"305084614=
-17062007"></SPAN></FONT>=A0</DIV> <DIV><FONT face=3D"Arial" size=3D"2"><SP=
AN class=3D"305084614-17062007">A sequence t of positive integers is=A0the =
trace of a perm if and only if t has infinitely many 1's.=A0 Let T be the s=
et of all such t.</SPAN></FONT></DIV> <DIV><FONT face=3D"Arial" size=3D"2">=
<SPAN class=3D"305084614-17062007"></SPAN></FONT>=A0</DIV> <DIV><FONT face=
=3D"Arial" size=3D"2"><SPAN class=3D"305084614-17062007">Suppose t_p and t_=
q are traces of perms p and q.=A0 Can someone find a decent formula for t_r=
, where r is the composite perm p-of-q?</SPAN></FONT></DIV> <DIV><FONT face=
=3D"Arial" size=3D"2"><SPAN class=3D"305084614-17062007"></SPAN></FONT>=A0<=
/DIV> <DIV><FONT face=3D"Arial" size=3D"2"><SPAN class=3D"305084614-1706200=
7">I'd like to see such a formula -=A0it would define a group operation on =
the set T.=A0</SPAN></FONT></DIV> <DIV><FONT face=3D"Arial" size=3D"2"><SPA=
N class=3D"305084614-17062007"></SPAN></FONT>=A0</DIV> <DIV><FONT face=3D"A=
rial" size=3D"2"><SPAN class=3D"305084614-17062007">Clark Kimberling=A0=A0=
=A0=A0=A0=A0 </SPAN></FONT></DIV></BLOCKQUOTE></DIV><BR></DIV></BODY></HTML>
--Apple-Mail-1--101249128--