Sequence Pictures

[Leroy Quet]

>...
>I have had my interest resurrected in the following sequence recently.
>
>I would bet that it would look interesting represented as you have the 
>other sequences, given its recursive definition (a definition which 
>involves 2 as well).
>
>(Also, a closed-form definition is given below, unless I made a mistake 
>in 'discovering' it.)
>
>If someone graphically represents the sequence described below, and you 
>can post it to a website, please send me the link. I am curious now if it 
>would LOOK interesting...
>(Send no attachments, please.)

>....

Never mind.
I was actually able to do this by 'hand', by simply copy/pasting.
But the sequence increases so slowly that it would only be interesting if 
the graph had a great number of terms represented, all terms much 
compressed into a relatively small width (relative to the number of bits 
in largest term).

Still the sequence seems a natural sequence to be represented this way, 
given its recursive definition.


thanks,
Leroy Quet
   
> ...
>>Let A(1) = 1, a sequence with only a single element.
>>
>>Let A(m+1) =
>>{A(m), a(m)+1, A(m)},
>>
>>a concatenation, where a(m) is the m_th term of the sequence A(m).
>>
>>( A(m) has 2^m -1 elements. So a(m) is not the last element of A(m)
>>for m >= 2, it should be emphasized.)
>>
>>The sequence begins:
>>
>>1,2,1,3,1,2,1,2,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,2,1,2,1,3,1,2,1,... 
>.....