A173022 Number of numbers <= n whose binary representation is without isolated ones.

1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 16, 17, 17, 17, 18, 19, 19, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21

Offset: 0

Author

Reinhard Zumkeller, Feb 07 2010

Keywords

• base
• nonn

Examples

			a(20) = #{0,3,6,7,12,14,15} = #{0,11,110,111,1100,1110,1111} = 7.
		

Links

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

Crossrefs

Cf. A005251, A007088, A144795, A173021, A173023.

Programs

Mathematica

Accumulate[Array[Boole[FreeQ[Split[IntegerDigits[#, 2]], {1}]] &, 100, 0]] (* Paolo Xausa, Oct 15 2024 *)

Formula

a(A144795(n+1)) = a(A144795(n)) + 1.

a(2^n - 1) = A005251(n+2).

A173021(n) <= a(n) <= A173023(n).