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A122005 Triangle read by rows: n-th row starts with n and continues with 1/3 the previous value as long as that is an integer.

%I A122005 #10 Mar 04 2015 21:31:49
%S A122005 1,2,3,1,4,5,6,2,7,8,9,3,1,10,11,12,4,13,14,15,5,16,17,18,6,2,19,20,
%T A122005 21,7,22,23,24,8,25,26,27,9,3,1,28,29,30,10,31,32,33,11,34,35,36,12,4,
%U A122005 37,38,39,13,40,41,42,14,43,44,45,15,5,46,47,48,12,4,49,50,51,17
%N A122005 Triangle read by rows: n-th row starts with n and continues with 1/3 the previous value as long as that is an integer.
%C A122005 A fractal sequence, which is to 3 as A123390 is to 2. Row lengths are A051064 3^a(n) exactly divides 3*n. Or, 3-adic valuation of 3*n.
%F A122005 a(1) = 1, for n > 1, if 3|a(n-1) then a(n) = a(n-1)/3, otherwise a(n) = (max_{k<n} a(k)) + 1.
%e A122005 Triangle starts:
%e A122005 1;
%e A122005 2;
%e A122005 3, 1;
%e A122005 4;
%e A122005 5;
%e A122005 6, 2;
%e A122005 7;
%e A122005 8;
%e A122005 9, 3, 1;
%e A122005 10;
%e A122005 11;
%e A122005 12, 4;
%e A122005 13;
%e A122005 14;
%e A122005 15, 5;
%e A122005 16;
%t A122005 Flatten[Function[n,NestWhile[Append[#, Last[#]/3] &, {n}, Last[#]/3 == Floor[Last[#]/3] &]][#] & /@ Range[50]] (* _Birkas Gyorgy_, Apr 14 2011 *)
%Y A122005 Cf. A051064, A123390.
%K A122005 easy,nonn,tabf
%O A122005 1,2
%A A122005 _Jonathan Vos Post_, Oct 14 2006