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To get the 6th term, for example, note that 5th term has three (10 in ternary!) 1's, one (1) 0, etc., giving 10 1 1 0 1 2 2 1 1 2.
1

%I #19 Mar 25 2017 05:34:49

%S 2,12,1112,10112,11102112,10110122112,1110211011222112,

%T 10110122110211022112,1110211011222110122110222112,

%U 10110122110211022110112221101022112,11102110112221101221102221102110221101110222112

%N To get the 6th term, for example, note that 5th term has three (10 in ternary!) 1's, one (1) 0, etc., giving 10 1 1 0 1 2 2 1 1 2.

%H John Cerkan, <a href="/A001389/b001389.txt">Table of n, a(n) for n = 1..22</a>

%t a[1]=2; a[n_] := a[n] = FromDigits@ Flatten@ Table[ {IntegerDigits[ Length[e], 3], e[[1]]}, {e, Split[ IntegerDigits[ a[n - 1]]]}]; Array[a, 11] (* _Giovanni Resta_, Mar 25 2017 *)

%Y Cf. A001388.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, _Thomas L. York_

%E More terms from _Sean A. Irvine_, Jul 04 2012