[seqfan] Re: Conflicting versions of "no 4-term AP"

M. F. Hasler oeis at hasler.fr
Wed Jan 6 16:57:15 CET 2016

On Mon, Jan 4, 2016 at 4:58 PM, Neil Sloane <njasloane at gmail.com> wrote:

> Summary of increasing sequences avoiding arithmetic progressions of
> specified lengths (the second of each pair is obtained by adding 1 to the
> first):
> 3-term AP: A005836 (>=0), A003278 (>0);

4-term AP: A005839 (>=0), A005837 (>0);
> 5-term AP: A020654 (>=0), A020655 (>0);
> 6-term AP: A020656 (>=0), A005838 (>0);
> 7-term AP: A020657 (>=0), A020658 (>0);
> 8-term AP: A020659 (>=0), A020660 (>0);
> 9-term AP: A020661 (>=0), A020662 (>0);
> 10-term AP: A020663 (>=0), A020664 (>0).
> These all now have consistent definitions and offsets.

(At least) the first of these had the %E

Offset corrected by njas, Mar 02 2008. This may require some of the
formulae to be adjusted.
The  second part of the line has disappeared, but several formulae remain
broken (at least those with "a(0)=0")
and many contributions were required to be prefixed by "If the offset was
changed to 0,...."

We have other cases where the sequence is named "List of numbers..."
(explicitly or implicitly) but it had been decided that, for logical /
mathematical / other reasons, it was better to retain offset 0.
And we have also the rule that in case of doubt, the name is adjusted to
the data and not vice versa.
This sequence might be an example where retaining the original offset 0
could have made sense.

But since the choice was different, this and probably some others from the
above list require some more corrections, until the day on which 0's right
to be the starting index of all these sets will be re-established...


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