# Recurrence relation for A043569?

Gottfried Helms Annette.Warlich at t-online.de
Sun Apr 23 08:13:28 CEST 2006

```Am 22.04.2006 01:16 schrieb Alonso Del Arte:
> I've just sent through the form a Mathematica command to calculate the
> terms of A043569. It involves multiplying Mersenne numbers by powers
> of 2 and sorting. It works but it's not terribly elegant.
>
> Is there a recurrence relation for this sequence? I've tried several
> different things along the lines of
>
> a(1) = 2, a(n) = a(n -1) + log_2 a(n - 1) + log_2 a(n - 2) etc., etc.,
>
> and they work except after a(n - 1) becomes a power of two, or before.
> Any suggestions?
>
> Al
>
>
>
Hmm, it looks like a list of lists, like

oo     oo
list  list (2^p-1)2^q
q=1    p=1

or (in binary)
1     10     100    1000    10000 ....
11    110    1100   11000   110000 ....
111   1110   11100  111000  1110000 ....
1111  11110  111100 1111000 11110000 ....
...
(ignoring the first column) plus an ordering operation.

The ordering operation seems simply to be the
rule to read this along the antidiagonal:
1
10
11
100
110
111
1000
1100
1110
1111
and omitting the elements 1,11,111,1111,...

But I don't have an idea actually to formulate
this in terms of indices of a sequence a(n)

Gottfried

```