[seqfan] Re: The Sequencer OEIS survey
M. F. Hasler
oeis at hasler.fr
Tue Apr 14 23:21:19 CEST 2015
The conjecture about A231002 is more or less explained in the sequence,
but incorrectly stated as "the sequence has a period of 28".
What is meant is that the characteristic sequence of these years has a
period of 28, i.e., n>0 is in the sequence iff n+28 is in the
sequence, and since 5 and 23 (= -5 (mod 28)) are the only terms <= 28,
this is the sequence of numbers congruent to +/- 5 (mod 28).
(strikingly similar to the sequence of numbers = +- 1 (mod 9^3), cf.
Robert Israel's reply.)
I added the formulas and may add a link to this post which has a link
to the sequencer survey website.
Concerning A169627 "A conjectured sequence of bud numbers for
eucalyptus flowers."
The given terms match other sequences than n^2+n+1, in particular one
of the toothpick sequences, which might well be the better match, in
view of the similar construction principle. (Astonishingly, the
matching one is a "hexagonal variant", while one of the illustrations
ressembles a lot to the original Toothpick sequences, at a first
glance.)
Concerning A152929, the formula (163 F_n + 63 L_n)/2 can be further reduced
using L(n)=F(n+1)+F(n-1) and successively F(n-1)+F(n)=F(n+1),
to: a(n)=50*fibonacci(n)+63*fibonacci(n+1)
(= 37*fibonacci(n+2)+13*fibonacci(n+3) = 24*fibonacci(n+2)+13*fibonacci(n+4)...)
(more to follow)
--
Maximilian
On Sun, Apr 12, 2015 at 6:28 AM, Philipp Emanuel Weidmann
<pew at worldwidemann.com> wrote:
> Back in February I announced a project to scan all OEIS sequences using
> the Sequencer system (https://github.com/p-e-w/sequencer) in order to
> identify new closed-form expressions for the sequence terms.
>
> The search has now concluded and the results are available at
> http://worldwidemann.com/the-sequencer-oeis-survey/
>
> Please note that only sequences without a "formula" field were scanned
> as explained in the article.
>
> Best regards
> Philipp Emanuel Weidmann
>
>
>
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