[seqfan] Re: Purely algorithmic number sequence identification

[Antti Karttunen]

Neither any success with A000265
http://www.sequenceboss.org/?q=1%2C+1%2C+3%2C+1%2C+5%2C+3%2C+7%2C+1%2C+9%2C+5%2C+11%2C+3%2C+13%2C+7%2C+15%2C+1%2C+17
(or the associated A003602)

Nor with sequences like:
https://oeis.org/A126760
or:
https://oeis.org/A254104
(nor its inverse A254103).


These kinds of sequences are very common in OEIS, where one doesn't
recurse with some constant offset decremented from n (as in a(n-1) +
a(n-2)) but with n/2 (if n is even) and say, with (n-1)/2 if n is odd.

Maybe also some "p-adic primitives" would be good, e.g. applying A007814 ?


Best,

Antti


On Wed, Feb 25, 2015 at 10:12 AM, Antti Karttunen
<antti.karttunen at gmail.com> wrote:
> On Tue, Feb 24, 2015 at 3:06 PM,  <seqfan-request at list.seqfan.eu> wrote:
>
>> Message: 12
>> Date: Mon, 23 Feb 2015 19:21:07 +0100
>> From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
>> To: seqfan at list.seqfan.eu
>> Subject: [seqfan]  Re: Purely algorithmic number sequence
>>         identification
>> Message-ID: <1424715667.2631.30.camel at worldwidemann.com>
>> Content-Type: text/plain; charset="UTF-8"
>>
>> Well, it turns out the first eight elements of A000001 satisfy the, umm,
>> "slightly exotic" recurrence relation
>>
>>   a(1) = 1
>>   a(2) = 1
>>   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>>
>> ;)
>>
>> In earnest, while I doubt that brute forcing formulas will bring any
>> insight into sequences that have baffled mathematicians for centuries
>> with their irregularity, what might indeed be interesting is to run the
>> system not on one sequence, but on tens of thousands, all of which have
>> no closed-form expression associated with them (is there a way to query
>> those on OEIS?). In a matter of days, Sequencer would likely return a
>> hundred or so closed forms, some of which may prove correct, which could
>> then be investigated rigorously.
>>
>> For such a search, I should probably also add a lot more combinatorial
>> and number theoretic primitives to the formula generator – whenever I
>> randomly browse around OEIS, most of the sequences seem to be counting
>> problems of some kind.
>
> Kudos for interesting development!
>
> Yes, especially number theoretic primitives would be welcome, because
> for now your system does not exactly shine on any such sequences. For
> example, although it correctly identifies factorials:
>
> http://www.sequenceboss.org/?q=1%2C2%2C6%2C24%2C120%2C720%2C5040
>
> then for primorials https://oeis.org/A002110 it remains baffled:
> http://www.sequenceboss.org/?q=1%2C+2%2C+6%2C+30%2C+210%2C+2310%2C+30030%2C+510510%2C+9699690
>
> Neither any success with the squares of primes:
> http://www.sequenceboss.org/?q=4%2C+9%2C+25%2C+49%2C+121%2C+169%2C+289
>
> (Not to speak about any of A000005, A000010 or A000203).
>
> Now, when testing the third row of "Ludic array"
> https://oeis.org/A255127
>
> http://www.sequenceboss.org/?q=5%2C+19%2C+35%2C+49%2C+65%2C+79%2C+95%2C+109%2C+125%2C+139%2C+155%2C+169
>
> the SequenceBoss, guesses a working recurrence for it:
>
> a_1 = 5, a_2 = 19, a3 = 35, a_n = a_{n-2} - a_{n-3} + a_{n-1} for n >= 4
>
> (This mirrors the recurrence a(n) = a(n-1) + a(n-2) - a(n-3), n>=4
> given for A007310 by Roger Bagula)
>
>
> No such success with the later rows of A255127 though:
>
> http://www.sequenceboss.org/?q=7%2C+31%2C+59%2C+85%2C+113%2C+137%2C+163%2C+191%2C+217%2C+241
>
> http://www.sequenceboss.org/?q=11%2C++55%2C+103%2C+151%2C+203%2C+251%2C++299%2C++343%2C++391%2C++443
>
> (although when looking at their graphs, they all look awfully linear...)
>
>
> Cheers,
>
> Antti
>
>>
>> Best regards
>> Philipp
>>