[seqfan] Re: Style sheet about offset
njasloane at gmail.com
Sun Dec 30 17:23:15 CET 2018
The answer is simple, and there is a very good reason. The reason is a
decision I made 50 years ago.
All the sequences are arranged lexicographically, but to do that they have
to be lined up, and I decided to line them up so the first field they are
sorted on is the first term >= 2 in magnitude
You can't compare the Fib numbers and the primes unless you line them up
0 1 1 2 3 5 8 13 ...
2 3 5 7 11 13 ...
You mark the first term > 1 in magnitude with asterisks (this is the
0 1 1 *2* 3 5 8 13 ... (second offset is 4)
bbbbb*2* 3 5 7 11 13 ... (b means a blank character) (second offset is 1)
and now can compare them . They are out of order! The correct order is
bbbbb*2* 3 5 7 11 13 ...
0 1 1 *2* 3 5 8 13 ...
The primes come before the Fib numbers.
You can still see this arrangement today, look at the line in any entry
"Sequence in context" That shows you the three sequences before and after
the one you are looking at, in the lex, order.
Let me give you an example, picked at random from a window I have open:
For A219585, the sequence is
1, 1, 1, 1, 1, 1, 1, *2*, 1, 1, 1, 5, 5, 2, 1, 1, 15, 40, 17, 2, 1, 1, 52,
which has offset line 0,8
meaning that when we sort it we begin comparing at the 8th field, the 2
that I marked with asterisks. The OEIS entry has these two lines. You can
probably guess what the second line is.
Sequence in context: A181783 <https://oeis.org/A181783> A121395
<https://oeis.org/A121395> A275377 <https://oeis.org/A275377> * A292464
<https://oeis.org/A292464> A090628 <https://oeis.org/A090628>A054387
Adjacent sequences: A219582 <https://oeis.org/A219582> A219583
<https://oeis.org/A219583> A219584 <https://oeis.org/A219584> * A219586
<https://oeis.org/A219586> A219587 <https://oeis.org/A219587>A219588
The first line tells you that sequences A275377 and A292464 are very close
to that one in the ordering.
OK, now to answer your question. If all terms are less than 2 in
magnitude, you can't sort them like this. So those get sorted on the first
field. Get it? This makes perfect sense.
I think you are confusing the first offset and the second offset. Of
course the first offset is meaningful for a 0 -1 +1 sequence. But the
second is not.
Incidentally, there seems to be a bug in the system. For A79, powers of 2,
those two lines are:
Sequence in context: A120617 <https://oeis.org/A120617> A131577
<https://oeis.org/A131577> A155559 <https://oeis.org/A155559> A171449
<https://oeis.org/A171449> A122803 <https://oeis.org/A122803> A274867
<https://oeis.org/A274867> A274866 <https://oeis.org/A274866>
Adjacent sequences: A000076 <https://oeis.org/A000076> A000077
<https://oeis.org/A000077> A000078 <https://oeis.org/A000078> * A000080
<https://oeis.org/A000080> A000081 <https://oeis.org/A000081>A000082
The asterisk is missing from the first line! Russ?
On Sun, Dec 30, 2018 at 8:49 AM Joerg Arndt <arndt at jjj.de> wrote:
> In http://oeis.org/wiki/Style_Sheet#Offset
> we say
> "There is a second part to the offset after a comma, which is the
> 1-based index of the first term which is greater than 1 in absolute
> So far, so good. But then:
> "If all terms are -1, 0, or 1 the second part should be 1."
> Why on earth is the counter-intuitive (and IMO plain illogical)
> part there?
> Best regards, jj
> Seqfan Mailing list - http://list.seqfan.eu/
More information about the SeqFan