[seqfan] Mystery tour with a(n)=sigma(a(n-1))

[Eric Angelini]

Hello SeqFans,
... might A007497 and A051572 converge in the (far, far)
future at some point?

They have the same definition a(n)=sigma(a(n-1)), but
different starts:

   http://www.research.att.com/~njas/sequences/A007497
   http://www.research.att.com/~njas/sequences/A051572

If we start with 9,13,14,22,23,... we'll bump into A007497  
If we start with 10,11,17,18,39,... we'll join A051572  

But what about starting with 16? Where does it go?
16->31->32->63->104->210->576->1651->1792->4088->8880...

More (mysterious so far) starts:
19->20->42->96->252->728->1680->5952->16256->32640...
27->40->90->234->546->1344->4064->8064->26520...

I've used this b-file (from A000005):
http://www.research.att.com/~njas/sequences/b000203.txt

Best,
É.