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

1,73

Links

Table of n, a(n) for n=1..102.

Eric Weisstein's World of Mathematics, Digit Block

Formula

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

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 *)

Crossrefs

Cf. A007088 (binary expansion).

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

Sequence in context: A278907 A037910 A162781 * A294079 A114117 A144435

Adjacent sequences: A056972 A056973 A056974 * A056976 A056977 A056978

Keyword

nonn,base,easy

Author

Eric W. Weisstein

Status

approved