A173023 Number of numbers <= n whose binary representation contains no isolated digits "11".

1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 9, 9, 9, 10, 11, 12, 13, 14, 14, 15, 16, 16, 17, 17, 17, 17, 17, 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 26, 27, 28, 29, 30, 30, 30, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 41, 42, 42, 43, 44, 44, 45, 46, 47

Offset: 0

Author

Reinhard Zumkeller, Feb 07 2010

Keywords

• base
• nonn

Examples

			a(20) = #{0,1,2,4,5,7,8,9,10,14,15,16,17,18,20} = #{0,1,10,100,101,111,1000,1001,1010,1110,1111,10000,10001,10010,10100} = 15.
		

Links

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

Crossrefs

Cf. A007088, A173021, A173022, A173025.

Programs

Mathematica

Accumulate[Table[If[Count[Split[IntegerDigits[n,2]],{1,1}]>0,0,1],{n,0,80}]] (* Harvey P. Dale, Feb 12 2017 *)

Formula

a(A173025(n+1)) = a(A173025(n)) + 1.

A173021(n) <= A173022(n) <= a(n).