%I #12 Mar 04 2020 22:49:45

%S 0,1,2,1,3,2,2,1,4,3,2,3,3,2,2,1,5,4,4,3,3,2,3,4,4,3,2,3,3,2,2,1,6,5,

%T 4,5,4,5,3,4,4,3,2,3,3,4,4,5,5,4,4,3,3,2,3,4,4,3,2,3,3,2,2,1,7,6,6,5,

%U 4,5,6,5,4,5,6,5,3,4,4,5,5,4,4,3,3,2,3,4,4,3,5,4,5,4,5,6,6,5,4,5,4,5,3,4,4

%N Number of times n must be differentiated to reach 0.

%H Reinhard Zumkeller, <a href="/A038571/b038571.txt">Table of n, a(n) for n = 0..10000</a>

%t dtn[ L_ ] := Fold[ 2#1+#2&, 0, L ]; f[ n_ ] := dtn[ Map[ Abs[ #[ [ 1 ] ]-#[ [ 2 ] ] ]&, Partition[ IntegerDigits[ n, 2 ], 2, 1 ] ] ]; g[ n_ ] := Length[ FixedPointList[ f, n ] ]-2; Table[ g[ n ], {n, 0, 120} ]

%o (Haskell)

%o a038571 n = snd $ until

%o ((== 0) . fst) (\(x, i) -> (fromIntegral $ a038554 x, i + 1)) (n, 0)

%o -- _Reinhard Zumkeller_, Mar 06 2013

%Y Cf. A038554.

%K nonn,easy,nice

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Erich Friedman_