A056979 Number of blocks of {1, 0, 1} in binary expansion of n.

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 2, 3, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0

Offset

1,21

Comments

a(n) = A213629(n,5) for n > 4. - Reinhard Zumkeller, Jun 17 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

J.-P. Allouche, J. Shallit, The Ring of k-regular Sequences II

Eric Weisstein's World of Mathematics, Digit Block

Index entries for sequences related to binary expansion of n

Formula

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

Mathematica

a[1] = a[2] = 0; a[n_] := a[n] = If[EvenQ[n], a[n/2], a[(n - 1)/2] + Boole[Mod[(n - 1)/2, 4] == 2]]; Table[a[n], {n, 1, 102}] (* Jean-François Alcover, Oct 22 2012, after Ralf Stephan *)

Prog

(Haskell)
import Data.List (tails, isPrefixOf)
a056979 = sum . map (fromEnum . ([1, 0, 1] `isPrefixOf`)) .
                    tails . a030308_row
-- Reinhard Zumkeller, Jun 17 2012
(PARI) a(n) = hammingweight(bitnegimply(bitand(n, n>>2), n>>1));
vector(102, i, a(i))  \\ Gheorghe Coserea, Sep 17 2015

Crossrefs

Cf. A014082, A056974, A056975, A056976, A056977, A056978, A056979, A056980.

Sequence in context: A035200 A198066 A141664 * A087812 A288384 A113045

Adjacent sequences: A056976 A056977 A056978 * A056980 A056981 A056982

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved