[seqfan] Re: A question about types of sequences

[Antti Karttunen]

On 8/11/19, Ali Sada via SeqFan <seqfan at list.seqfan.eu> wrote:
> Hi Everyone,
> Are there any resources I can read about types of sequences? For example
> there are sequences where a(n) depends on n, there are sequences where a(n)
> depends on a(n-1), etc. I would appreciate any recommendations.

You may start from https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Properties
but I guess it only lists a small part what is possible (with emphasis
on number theory), because Z^N is uncountable, after all.

Then there are also lots of sequences of type "Lexicographically
earliest sequence that satisfies a <certain condition>".

Of course a sequence may fulfill the criteria of several ad-hoc
classes simultaneously.

I have found it productive to consider recurrences of more general
kind, like a(n) = f(a(Axxxxxx(n))), where f is some integer-valued
function and Axxxxxx is some "meaningful" operation acting on n
(usually already submitted as a sequence, like e.g., A003557, A028234
or A064989), instead of just the common operations like n-1, n-k or
floor(n/2).


> Best,
> Ali

Best regards,

Antti