A056975 Number of blocks of {0, 0, 1} in binary expansion of n.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base
• easy

Links

• Eric Weisstein's World of Mathematics, Digit Block

Crossrefs

Cf. A007088 (binary expansion).

Other block counts: A014082, A056974, A056976, A056977, A056978, A056979, A056980.

Programs

Mathematica

a[n_, bits_] := (idn = IntegerDigits[n, 2]; ln = Length[idn]; lb = Length[bits]; For[cnt = 0; k = 1, k <= ln - lb + 1, k++, If[idn[[k ;; k + lb - 1]] == bits, cnt++]]; cnt); Table[ a[n, {0, 0, 1}], {n, 1, 102} ] (* Jean-François Alcover, Oct 23 2012 *)
Table[SequenceCount[IntegerDigits[n,2],{0,0,1}],{n,110}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 26 2019 *)

Formula

a(2n) = a(n), a(2n+1) = a(n) + [n congruent to 0 mod 4]. - Ralf Stephan, Aug 22 2003