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A214972 a(n) = a(floor(2*(n-1)/3)) + 1, where a(0) = 0.

%I A214972 #30 Oct 31 2012 09:32:59
%S A214972 0,1,1,2,2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,
%T A214972 6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,
%U A214972 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9
%N A214972 a(n) = a(floor(2*(n-1)/3)) + 1, where a(0) = 0.
%H A214972 Clark Kimberling, <a href="/A214972/b214972.txt">Table of n, a(n) for n = 0..10000</a>
%F A214972 Conjecture:  a(n) = a(n-1) + 1 if n is in A152009, and a(n) = a(n-1) otherwise.
%e A214972 a(10) = a(9*2/3)+1 = a(6)+1 = 3+1 = 4.
%t A214972 a[0] := 0; a[n_] := a[Floor[2*(n-1)/3]] + 1; Table[a[n], {n, 0, 120}]
%o A214972 (PARI) a214972(n) = {local(nn,r); nn=n; r=0; while(nn>0, r=r+1; nn=floor(2*(nn-1)/3)); r} \\ _Michael B. Porter_, Oct 30 2012
%o A214972 (Maxima)
%o A214972 a[0]:0$
%o A214972 a[n]:=a[floor(2*(n-1)/3)] + 1$
%o A214972 A214972(n):=a[n];
%o A214972 makelist(A214972(n),n,0,30); /* _Martin Ettl_, Oct 31 2012 */
%K A214972 nonn
%O A214972 0,4
%A A214972 _Clark Kimberling_, Oct 19 2012