[seqfan] Re: Permutations (Was: Evaluating sequences by same terms and different indices)

[Antti Karttunen]

On Sun, Mar 8, 2015 at 9:43 AM, Antti Karttunen
<antti.karttunen at gmail.com> wrote:
> On Sun, Mar 8, 2015 at 12:33 AM,  <seqfan-request at list.seqfan.eu> wrote:
>
>> Message: 3
>> Date: Thu, 5 Mar 2015 21:39:13 -0600
>> From: "Bob Selcoe" <rselcoe at entouchonline.net>
>> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>> Subject: [seqfan] Re: Evaluating sequences by same terms and different
>>         indices
>> Message-ID: <D8F38AB413E046BFA770495A115CEF1D at OwnerPC>
>> Content-Type: text/plain; format=flowed; charset="utf-8";
>>         reply-type=original
>>
>> Hi Frank,
>>
>> Thanks for the reply.  The issue isn't how to show the indexing; it's to
>> describe the comparisons.
>>
>> For instance, A064413 and A255582.  What would f and g be that would express
>> their similarity?  What are the "explicit formulas"??
>
> Submit for example a(n) = A064413(A255479(n)) [where A255479 is the
> inverse permutation of A255582] and also its inverse b(n) =
> A255582(A064664(n)) [where A064664 is the inverse of A064413]. If the
> resulting graphs stay "near" the diagonal y=x, then the permutations
> A064413 and A255582 are quite "similar" in some respect. Also, find
> the fixed points of a [equally, the fixed points of its inverse b],
> i.e. those n for which a(n) = n.

These (fixed points) would then give the zeros of a(n) - n, i.e., the
zeros of the sequence http://oeis.org/A255482

A.

>
> This has in general proved to be a good technique of finding
> interesting new sequences. First I'm just slightly irritated by some
> common property of two sequences, permutations or tables, and almost
> brush it aside as an irrelevant coincidence, but then, when I start
> computing sequences based on that, suddenly something interesting can
> be found.
> For a quite recent example, see e.g.:
> https://oeis.org/A241912
> and
> https://oeis.org/A249821
>
>
> Best regards,
>
> Antti
>
>
>
>>
>> Bob S
>>
>> --------------------------------------------------
>> From: "Frank Adams-Watters" <franktaw at netscape.net>
>> Sent: Thursday, March 05, 2015 7:34 PM
>> To: <seqfan at list.seqfan.eu>
>> Subject: [seqfan] Re: Evaluating sequences by same terms and
>> differentindices
>>
>>> I don't quite see the problem. You can enter a formula like:
>>>
>>> a(f(n)) = b(n) or a(n) = b(g(n)) or even a(f(n)) = b(g(n))
>>>
>>> (where f and g are explicit formulas, and b is an A-number).
>>>
>>> What further description do you need?
>>>
>>> Franklin T. Adams-Watters
>>>