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

1,3

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A072085.

Sequence in context: A359312 A179868 A104232 * A180094 A333870 A354914

Adjacent sequences: A072083 A072084 A072085 * A072087 A072088 A072089

Keyword

nonn

Author

Reinhard Zumkeller, Jun 14 2002

Status

approved