A123390 - OEIS

%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