%I #10 Oct 09 2015 18:00:52
%S 1,2,1,3,4,2,1,5,6,3,7,8,4,2,1,9,10,5,11,12,6,3,13,14,7,15,16,8,4,2,1,
%T 17,18,9,19,20,10,5,21,22,11,23,24,12,6,3,25,26,13,27,28,14,7,29,30,
%U 15,31,32,16,8,4,2,1,33,34,17,35,36,18,9,37,38,19,39,40,20,10,5,41,42,21
%N Triangle read by rows: n-th row starts with n and continues with half the previous value as long as that is even.
%C A fractal sequence, generated by the rule a(n) is a new maximum when a(n-1) is odd and a repetition of an earlier value when a(n-1) is even.
%H Alois P. Heinz, <a href="/A123390/b123390.txt">Rows n = 1..10000, flattened</a>
%F a(1) = 1, for n > 1, if a(n-1) is even, a(n) = a(n-1)/2, otherwise a(n) = (max_{k<n} a(k)) + 1.
%F Ordinal transform of A082850.
%e Triangle starts
%e 1;
%e 2, 1;
%e 3;
%e 4, 2, 1;
%e 5;
%e 6, 3;
%e 7;
%e 8, 4, 2, 1;
%e 9;
%e 10, 5;
%e 11;
%e 12, 6, 3;
%e 13;
%p T:= proc(n) local m,l; m:=n; l:= m;
%p while irem(m, 2, 'm')=0 do l:=l,m od: l
%p end:
%p seq(T(n), n=1..40); # _Alois P. Heinz_, Oct 09 2015
%t Flatten[Function[n, NestWhile[Append[#, Last[#]/2] &, {n}, EvenQ[Last[#]] &]][#] & /@ Range[20]] (* _Birkas Gyorgy_, Apr 13 2011 *)
%Y Row lengths are A001511. Cf. A120385.
%K nonn,tabf
%O 1,2
%A _Franklin T. Adams-Watters_, Oct 13 2006