A063250 - OEIS

%I #40 Apr 26 2024 06:08:39

%S 0,0,1,0,2,2,1,0,3,3,3,3,2,2,1,0,4,4,4,4,4,4,4,4,3,3,3,3,2,2,1,0,5,5,

%T 5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,3,3,3,3,2,2,1,0,6,6,6,6,

%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5

%N Number of binary right-rotations (iterations of A038572) to reach fixed point.

%C a(n) = 0 when n is a fixed point of form 2^k-1 left-rotation analog appears to be same as A048881.

%F If n+1 is a power of 2 then a(n)=0 otherwise a(n) = 1 + a(floor(n/2)).

%F Conjectured g.f.: 1/(1-x) * Sum_{j>=0} x^(2^j) - (1-x^(2^j)) * Sum_{k>=1} x^((2^j)*(2^k-1)). - _Mikhail Kurkov_, Sep 29 2019

%e a(11)=3 since under right-rotation 11 -> 13 -> 14 -> 7 and 7 is a fixed point.

%t Table[Length[FixedPointList[FromDigits[RotateRight[IntegerDigits[ #,2]], 2]&, n]]-2,{n,0,110}] (* _Harvey P. Dale_, Dec 23 2011 *)

%o (Python)

%o def a(n):

%o     if n<2: return 0

%o     b=bin(n)[2:]

%o     s=0

%o     while "0" in b:

%o         N=int(b[-1] + b[:-1], 2)

%o         s+=1

%o         b=bin(N)[2:]

%o     return s

%o print([a(n) for n in range(105)]) # _Indranil Ghosh_, May 25 2017

%Y Cf. A038572, A048881.

%K base,easy,nonn

%O 0,5

%A _Marc LeBrun_, Jul 11 2001