A038571 Number of times n must be differentiated to reach 0.

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, 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, 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

Offset

0,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Mathematica

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} ]

Prog

(Haskell)
a038571 n = snd $ until
   ((== 0) . fst) (\(x, i) -> (fromIntegral $ a038554 x, i + 1)) (n, 0)
-- Reinhard Zumkeller, Mar 06 2013

Crossrefs

Cf. A038554.

Sequence in context: A333766 A333226 A175548 * A008687 A290251 A080801

Adjacent sequences: A038568 A038569 A038570 * A038572 A038573 A038574

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Erich Friedman

Status

approved