Re "need self-contained definition", etc

Thu Jul 17 13:23:51 CEST 2008

since a(0) is really not defined.  I'll correct that.
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Date: Thu, 17 Jul 2008 16:13:12 +0200
From: "=?ISO-8859-1?Q?Beno=EEt_Jubin?=" <benoit.jubin at gmail.com>
To: njas at research.att.com
Subject: Re: A036236 and A078457
Cc: pxp at rogers.com, seqfan at ext.jussieu.fr
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Speaking of A036236, I see that A122182 is defined as "a bisection of
A036236".  I assume that it means A122182(n)=A036236(2n).  But then
A122182 should begin with 1 (which should be inserted before 3).
Also, it is strange to define a sequence with the undefined article
"a".  So I would propose:

%I A122182
%N A122182 Least number m such that 2^m (mod m) = 2n, or 0 if no such k exists.
%C A122182 A bisection of A036236: a(n) = A036236(2n).

%I A124977
%N A124977 Least number m such that 2^m (mod m) = 2n+1, or 0 if no
such k exists.
%C A124977 A bisection of A036236: a(n) = A036236(2n+1).

Also, the definition of A036236 contains "a(0) = 1 by convention". I
think this is superfluous: no convention is needed since this follows
from the definition. To be consistent with the two sequences above,
one could write:

%I A036236
%N A036236 Least number m such that 2^m (mod m) = n (least inverse of
A015910), or 0 if no such k exists.

What do you think?

Benoit

On Thu, Jul 17, 2008 at 1:39 PM, N. J. A. Sloane <njas at research.att.com> wrote:
> Hans, You said:
> Last year I submitted a ten-thousand value "b-file" for A036236. The
> link to it says only one-thousand: that can be fixed.
>
> Me:  b-files are supposed to be absolutely correct. But for A036236 the
> value of a(69) is presently unknown, and your file gives the value
> of -1 for n=69.
>
> That's why the link looks like this:
>
> %H A036236 Hans Havermann, <a href="http://www.research.att.com/~njas/sequences/a036236.txt">Ta\
> ble of n, a(n) for n = 1..1000 with -1 for those entries where a(n) > 10^11</a>
>
> The file is called a036236.txt (not b036236.txt) - and that's probably why
> i shortened it to 1000 terms from 10000.
>
> You also said:
>
> For A078457, Why is a(0) = 3, and not 1?
>
> Me:  A036236 has offset 1, and I guess A078457 should have offset 1 too,
> since a(0) is really not defined.  I'll correct that.
>
> Best regards
>
> Neil
>

On Jul 17, 2008, at 7:39 AM, N.J.A. Sloane wrote:

> b-files are supposed to be absolutely correct. But for A036236 the  
> value of a(69) is presently unknown, and your file gives the value  
> of -1 for n=69.
>
> That's why the link looks like this:
>
> %H A036236 Hans Havermann, <a href="http://www.research.att.com/~njas/sequences/a036236.txt 
> ">Table of n, a(n) for n = 1..1000 with -1 for those entries where  
> a(n) > 10^11</a>
>
> The file is called a036236.txt (not b036236.txt) - and that's  
> probably why i shortened it to 1000 terms from 10000.

You didn't shorten my file. To quote your email to me of 19 April  
2007: "I downloaded your file http://chesswanks.com/seq/b036236.txt,  
converted all the control-M characters to back-slash 012 and changed  
its name to a036236, and added it to the OEIS web site in place of Bob  
Wilson's file." You just didn't change Bob Wilson's link-description  
of 1000 to the actual 10000. Today, the link looks like this:

> Joe K. Crump, 2^n mod n %Y%H A036236 Hans Havermann, Table of n,  
> a(n) for n = 1..1000 with -1 for those entries where a(n) > 10^11

... which is different (I think) from yesterday by the introduction of  
"%Y%H A036236" instead of a line-return, but the incorrect "1000" is  

With regard to a(69) being "presently unknown" (i.e., the b-file being  
not "absolutely correct"), I assume you mean that there is a  
possibility that a(69) might not exist and that, therefore, a value of  
-1, implying a(n) > 10^11, suggests otherwise. In fact, a(n) > 10^11  

For those who might be interested, I've got my b-file for A078457  
(assuming my cable isn't out... they're replacing gas-pipes on the  

http://chesswanks.com/seq/b078457.txt

I've added Jan-Christoph Schlage-Puchta's values for a(134), a(392),  
a(550), a(716), a(748), a(784), and a(980) because those values  
exceeded my 10^11 search-limit. I've made a(0) equal 1, replaced my  
original -1's with asterisks (to indicate non-entries) and added Joe  
Crump's maximum (preceded by <=) for a(34). Perhaps Jan-Christoph  
Schlage-Puchta can be persuaded to calculate this one for us.

Hans