Bell numbers

[Olivier Gerard]

On Thu, Jun 28, 2001 at 12:47:03PM -0400, Jeffrey Shallit wrote:
> 
> Somebody posted a message about the highest power of 2 dividing a 
> Bell number, but I accidently deleted it.  Could somebody send it
> to me again?  BTW, numerical experiments suggest this sequence
> is a 2-automatic sequence, so it may be generated by a very
> simple finite automaton.
> 
> Jeffrey Shallit
>

Dear Jeffrey,

I have looked at the whole seqfan archive (3 years now) and did not found the
message you refer to.
The most recent posting talking about Bell numbers what the announce
of a recent article of the JIS on generalisation of such and Stirling as well.

Anyway, the sequence exists in the EIS under A061462:


%I A061462
%S A061462 1,1,2,1,1,4,1,1,4,1,1,2,1,1,2,1,1,4
%N A061462 The exact power of 2 that divides the n-th Bell number (A000110).
%C A061462 It appears that a(n) = 1 if n = 0 or 1 mod 3 and that a pattern exists also for n = 2 mod 3 but I don't have a formula yet.
%Y A061462 Cf. A000110.
%K A061462 nonn
%O A061462 0,3
%A A061462 Ahmed Fares (ahmedfares at my-deja.com), Jun 10 2001

Maybe it was on math-fun ? I have no archive of this list sorry.

Olivier Gerard