A044933 Number of runs of even length in the base-2 representation of n.

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

Offset

1,12

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384 (terms 1..1000 from Harvey P. Dale)

Index entries for sequences related to binary expansion of n.

Formula

a(n) = A005811(n) - A044942(n). - Antti Karttunen, Oct 22 2025

Mathematica

Table[Count[Length/@Split[IntegerDigits[n, 2]], _?EvenQ], {n, 100}] (* Harvey P. Dale, Jun 20 2023 *)

Prog

(PARI) A044933(n) = { my(c=0, i=0, p=n%2); while(n, if((n%2)==p, i++, if(!(i%2), c++); i=1; p=n%2); n >>= 1); if(!(i%2), c++); (c); }; \\ Antti Karttunen, Oct 22 2025

Crossrefs

Cf. A005811, A044942.

Sequence in context: A172398 A070107 A299908 * A295343 A025915 A081285

Adjacent sequences: A044930 A044931 A044932 * A044934 A044935 A044936

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved