# Recurrence relation for A043569?

franktaw at netscape.net franktaw at netscape.net
Sat Apr 22 02:53:57 CEST 2006

```This sequence is twice A023758.  Take a look at the formulas there.

If you want to generate them in order, take differences of powers of 2, with the lower powers in reverse order:

2^2-2^1, 2^3-2^1, 2^3-2^2, ...

-----Original Message-----
From: Alonso Del Arte alonso.delarte at gmail.com

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
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