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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Links

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

Crossrefs

Cf. A038554.

Programs

Haskell

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

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} ]

Extensions

More terms from Erich Friedman