A175872 Write n in binary. Consider the 0's and 1 as a list. (*) If the new list consists entirely of 1's, then a(n) = the number of 1's, and end. Otherwise, construct a new list made up of the lengths, written in order, of the runs of similarly-valued terms from the previous list. Go to *.

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

Offset

1,2

Comments

n appears for the first time at A000975(n). - Sean A. Irvine and N. J. A. Sloane, Dec 02 2010

A217921(n) = number of steps needed to calculate a(n). - Reinhard Zumkeller, Mar 26 2013

Links

Sean A. Irvine, Table of n, a(n) for n = 1..100000

Example

100 (decimal) in binary is 1100100. The lengths of the runs are: 2,2,1,2. The lengths of the runs in the latest list are: 2,1,1. The lengths of the runs in the latest list are: 1,2. The lengths of the runs in the latest list are: 1,1. This last list consists entirely of 1's. There are two 1's, so a(100) = 2.

Mathematica

f[n_Integer] := IntegerDigits[n, 2]; f[nn:{1..}] := nn; f[nn_List] := Length /@ Split[nn]; a[n_] := FixedPoint[f, n] // Length; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 26 2013 *)

Prog

(Haskell)
import Data.List (group, genericLength)
a175872 = f . a030308_row where
   f xs | all (== 1) xs = length xs
        | otherwise     = f $ map genericLength $ group xs
-- Reinhard Zumkeller, Mar 26 2013

Crossrefs

Cf. A101211, A000975.

Cf. A030308.

Sequence in context: A164024 A145193 A292585 * A143117 A108053 A076221

Adjacent sequences: A175869 A175870 A175871 * A175873 A175874 A175875

Keyword

base,nonn,nice

Author

Leroy Quet, Oct 03 2010

Extensions

a(3) corrected by Leroy Quet, Oct 06 2010

More terms from Sean A. Irvine, Dec 02 2010

Status

approved