uned sequences (& preventing duplicate sequences follow-up)

[r.shepherd]

Frank, (Sequence Fans),

I finally dug up the one example that first came to mind when I wrote
the earlier message -- please see below.

I wrote:
> >  Something like this would be more beneficial than seeing two
> > "identical" entries that really aren't.
>

To which Frank Ellermann replied (in part):

> ACK, using three sequences with 1st = identical terms, 2nd =
> more terms, 3rd = different terms is an interesting idea.  Who
> tells superseeker about it ?  <gd&r>  That's no counterexample,
> but some things won't work as expected with your proposal.  I'd
> like to see these "continuation at first difference sequences",
> and probably the number of these cases is very small.  So if a
> lookup won't work directly there would be still references for
> a manual lookup of the different continuations.
>

I must confess that I didn't even think about superseeker when
suggesting the above.  Still, though, I think that appropriate
cross-references used with my suggestion would be an improvement
over the status quo -- even though you may be right that the number
of cases currently in the OEIS that could benefit from this may be
fairly small.

Here's that example (and, yes, I'm afraid these three sequences have the
base keyword).  Earlier, when I suggested to Neil that I thought these
sequences were duplicates, only A009996 had 3-digit terms, and
all 1- and 2-digit terms in the sequences were identical (except that
the A009996 begins with 0 and was missing the term 92).  I had thought
that perhaps the sense of one "<=" and ">=" was reversed by a single
typo in each of A032783 and A032907.  Apparently, they were
described as intended but didn't have enough terms to demonstrate the
described property.  Neil added the "differs" comments and more terms
after agreeing that they all three certainly looked alike (originally).

...so, the divergence doesn't happen now at the last term but there's
still certainly a lot of overlap -- making these good candidates for the
technique I was describing (I'm too lazy right now to change/extend them
myself in this way though.  :^) ).

%I A032873
%S A032873 1,2,3,4,5,6,7,8,9,10,11,20,21,22,30,31,32,33,40,41,42,43,44,
%T A032873 50,51,52,53,54,55,60,61,62,63,64,65,66,70,71,72,73,74,75,76,
%U A032873
77,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,100,101,102,103,
104,105,106,107,108,109,111,112
%N A032873 Base 10 representation SUM{d(i)*10^i: i=0,1,...,m) has d(m) >=
d(m-1) <= d(m-2) >= ...
%Y A032873 Contains 100 so differs from A032907, contains 101 so differs
from A009996.
%K A032873 nonn,base
%O A032873 1,2
%A A032873 Clark Kimberling, ck6(AT)evansville.edu

%I A032907
%S A032907 1,2,3,4,5,6,7,8,9,10,11,20,21,22,30,31,32,33,40,41,42,43,44,
%T A032907 50,51,52,53,54,55,60,61,62,63,64,65,66,70,71,72,73,74,75,76,
%U A032907
77,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,110,111,120
%N A032907 Base 10 representation SUM{d(i)*10^i: i=0,1,...,m} has d(0) <=
d(1) >= d(2) <= ...
%Y A032907 Differs from A032873 and A009996.
%K A032907 nonn,base
%O A032907 1,2
%A A032907 Clark Kimberling, ck6(AT)evansville.edu

%I A009996
%S A009996
0,1,2,3,4,5,6,7,8,9,10,11,20,21,22,30,31,32,33,40,41,42,43,44,50,51,
%T A009996
52,53,54,55,60,61,62,63,64,65,66,70,71,72,73,74,75,76,77,80,81,82,83,
%U A009996
84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,100,110,111,200,210,211
%N A009996 Digits in nonincreasing order.
%C A009996 Base 10 representation SUM{d(i)*10^i: i=0,1,...,m} has d(m) >=
d(m-1) >= ... >= d(1) >= d(0).
%C A009996 These numbers might be called "Nialpdromes".
%H A009996 E. W. Weisstein, <a
href="http://mathworld.wolfram.com/Digit.html">Link to a section of The
World of Mathema\
  tics.</a>
%Y A009996 Differs from A032873 and A032907.
%K A009996 nonn,base
%O A009996 0,3
%A A009996 njas
%E A009996 Corrected by Rick L. Shepherd (R.Shepherd(AT)prodigy.net), Jun 06
2002

Thanks,
Rick

>                        Bye, Frank