A072086 Number of steps to reach 1, starting with n and applying the A072084-map repeatedly.

0, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 2, 3, 3, 2, 2, 2, 3, 2, 3, 2, 2, 3, 1, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 1, 3, 3, 3, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 3, 2

Offset: 1

Author

Reinhard Zumkeller, Jun 14 2002

Keywords

• nonn

Examples

			n=21: '11'*'111' -> '10'*'11' -> '11'*'1' -> '1'; i.e., 21=3*7 -> 6=2*3 -> 2*1 -> 1*1=1, therefore a(21)=3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072085.

Programs

Haskell

a072086 n = fst $
   until ((== 1) . snd) (\(i, x) -> (i + 1, a072084 x)) (0, n)
-- Reinhard Zumkeller, Feb 10 2013

Maple

A072086 := proc(n) local c,i,j; c :=0; i := n;
while i > 1 do i:=A072084(i); c:=c+1 od; c end:
# Note that this gives A072086(0)=0 if desired
# without any additional case discrimination.
# Peter Luschny, Jan 16 2010

Mathematica

b[1] = 1; b[n_] := Times @@ Power @@@ (FactorInteger[n] /. {p_Integer, e_} :> {DigitCount[p, 2, 1], e}); a[n_] := Length[FixedPointList[b, n]] - 2; Array[a, 100] (* Jean-François Alcover, Feb 09 2018 *)