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

0,8

Links

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

Formula

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

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A029393 A275150 A303904 * A109703 A103375 A285758

Adjacent sequences: A173018 A173019 A173020 * A173022 A173023 A173024

Keyword

base,nonn,look

Author

Reinhard Zumkeller, Feb 07 2010

Status

approved