A217921 Number of steps to calculate A175872(n).

0, 1, 0, 2, 1, 2, 0, 2, 2, 1, 3, 3, 3, 2, 0, 2, 2, 4, 3, 3, 1, 4, 3, 2, 3, 3, 2, 2, 3, 2, 0, 2, 2, 4, 2, 2, 4, 3, 2, 3, 4, 1, 3, 4, 3, 4, 3, 2, 2, 4, 3, 3, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 0, 2, 2, 4, 2, 2, 4, 2, 3, 2, 2, 4, 5, 3, 4, 2, 2, 3, 4, 3, 3, 3, 1, 4

Offset: 1

Author

Reinhard Zumkeller, Mar 26 2013

Keywords

• nonn

Comments

a(A000225(n)) = 0; a(A000975(n)) = 1.

Examples

			n=100, 4 steps: [1,1,0,0,1,0,0]->[2,2,1,2]->[2,1,1]->[1,2]->[1,1], therefore a(100)=4, A175872(100)=2;
n=127, no step: [1,1,1,1,1,1,1], therefore a(127)=0, A175872(127)=7;
n=128, 2 steps: [1,0,0,0,0,0,0,0]->[1,7]->[1,1], therefore a(128)=2, A175872(128)=2;
n=129, 2 steps: [1,0,0,0,0,0,0,1]->[1,6,1]->[1,1,1], therefore a(129)=2, A175872(129)=3;
n=130, 4 steps: [1,0,0,0,0,0,1,0]->[1,5,1,1]->[1,1,2]->[2,1]->[1,2], therefore a(130)=4, A175872(130)=2;
n=131, 2 steps: [1,0,0,0,0,0,1,1]->[1,5,2]->[1,1,1], therefore a(131)=2, A175872(100)=3.
		

Links

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

Crossrefs

Cf. A030308.

Programs

Haskell

import Data.List (group, genericLength)
a217921 n = fst $ until (all (== 1) . snd) f (0, a030308_row n) where
   f (i, xs)  = (i + 1, map genericLength $ group xs)