A173021 Number of numbers <= n whose binary representation is without isolated ones or isolated double ones.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11

Offset: 0

Author

Reinhard Zumkeller, Feb 07 2010

Keywords

• base
• nonn
• look

Examples

			a(30) = #{0, 7, 14, 15, 28, 30} = #{0, 111, 1110, 1111, 11100, 11110} = 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005252, A007088, A173022, A173023, A173024.

Programs

Mathematica

ioQ[n_]:=Module[{idn2=Split[IntegerDigits[n,2]]},FreeQ[idn2,{1}]&&FreeQ[ idn2,{1,1}]]; Accumulate[Table[If[ioQ[n],1,0],{n,0,90}]] (* Harvey P. Dale, May 15 2016 *)

Formula

a(A173024(n+1)) = a(A173024(n)) + 1.

a(2^n - 1) = A005252(n+1).

a(n) <= A173022(n) <= A173023(n).