OEIS is running again

[Antti Karttunen]

Joshua Zucker wrote:

> On 5/23/06, Antti Karttunen <antti.karttunen at gmail.com> wrote:
>
>> Joshua Zucker wrote:
>>
>> > Some of the sequences you suggest have a very fractal-like appearance
>> > -- I wonder if there is some real way in which they are fractal!
>

Well, many of them are produced ultimately by fidgeting with the binary 
or some other "expansion" of n,
so indeed, they are fractal. I wonder to what degree _every_ recursive
sequence is fractal in some sense, because one creates an infinite 
amount of information
with just a finite formula.
E.g. A000027(1) = 1,
A000027(n+1) = A000027(n) + 1
Surely it's scale-invariant everywhere... ;-)

But, also many table-sequences seem to produce a characteristic pattern.


This is seen even in the table of GCD's:
http://www.research.att.com/~njas/sequences/table?a=3989&fmt=5
and LCM's
http://www.research.att.com/~njas/sequences/table?a=3990&fmt=5
although in somewhat "modulated" form.


Also, Pascal's triangle produces a nice graph:
http://www.research.att.com/~njas/sequences/table?a=7318&fmt=5
(Please wait so that program can dig the data from the extra terms file.)

I wonder whether there's really a pattern in some of the 
number-theoretic sequences, like
in A000005 (Tau, number of divisors of n):
http://www.research.att.com/~njas/sequences/table?a=5&fmt=5
(and it's GF(2)[X] analogue:
http://www.research.att.com/~njas/sequences/table?a=91220&fmt=5 )

and in these:
http://www.research.att.com/~njas/sequences/table?a=1222&fmt=5

http://www.research.att.com/~njas/sequences/table?a=1227&fmt=5
or whether I'm just prone to hallucinations.


Certain sign-sequences look nice:
http://www.research.att.com/~njas/sequences/table?a=110279&fmt=5

Distribution of the first primes are best seen in:
http://www.research.att.com/~njas/sequences/table?a=720&fmt=5


Terveisin,

Antti



>> >
>> > --Joshua
>> >
>>
>> Can I answer to this publicly, on SeqFan list?
>
>
> Sure, go ahead!
> --Joshua
>