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%I #9 Mar 04 2015 21:17:00
%S 1,2,1,1,3,1,2,1,2,1,1,1,4,1,2,1,1,3,1,2,1,1,3,1,2,1,2,1,2,1,1,1,1,5,
%T 1,2,1,1,3,1,2,1,2,1,1,1,4,1,2,1,1,3,1,2,1,2,1,1,1,4,1,2,1,1,3,1,2,1,
%U 1,3,1,2,1,1,3,1,2,1,2,1,2,1,2,1,1,1,1,1,6,1,2,1,1,3,1,2,1,2,1
%N A self-descriptive fractal sequence: if 1 is subtracted from every term and any zero terms are omitted, the original sequence is recovered (this process may be called "lower trimming").
%C This sequence is also self-descriptive, in that each element gives the number of zeros that were removed before it. The indices where the sequence hits a new maximum value (2 at the 2nd position, 3 at the 5th position, 4 at the 13th, 5 at the 34th, etc.) are every second Fibonacci number.
%t lowertrim[list_] := DeleteCases[list - 1, 0];
%t Nest[Flatten[Append[#, {ConstantArray[1, #[[Length[lowertrim[#]] + 1]]], #[[Length[lowertrim[#]] + 1]] + 1}]] &, {1, 2}, 15] (* _Birkas Gyorgy_, Apr 27 2011 *)
%Y Cf. A112378, A112379, A112380, A000045, A112382.
%K nonn,easy,nice
%O 0,2
%A _Kerry Mitchell_, Dec 04 2005
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