A277937 Number of runs of 1's of length 1 in the binary expansion of n.

0, 1, 1, 0, 1, 2, 0, 0, 1, 2, 2, 1, 0, 1, 0, 0, 1, 2, 2, 1, 2, 3, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 2, 2, 1, 2, 3, 1, 1, 2, 3, 3, 2, 1, 2, 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 2, 2, 1, 2, 3, 1, 1, 2, 3, 3, 2, 1, 2, 1, 1, 2, 3, 3, 2, 3, 4, 2

Offset

0,6

Comments

2^a(n) is the run length transform of 1,2,1,1,1,1,....

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Formula

a(2n) = a(n), a(4n+1) = a(8n+1) = a(n) + 1, a(8n+3) = a(n), a(8n+5) = a(2n+1) + 1, a(8n+7) = a(4n+3).

Example

a(25) = 1 since 25 = 11001_2 has one runs of 1's of length 1.

Mathematica

A292342[n_] := Count[Split[IntegerDigits[n, 2]], {1}];
Array[A292342, 100, 0] (* Paolo Xausa, Oct 01 2024 *)

Prog

(Python)
def A277937(n):
    return sum(1 for d in bin(n)[2:].split('0') if len(d) == 1)

Crossrefs

Sequence in context: A362426 A039971 A205593 * A334913 A112020 A069160

Adjacent sequences: A277934 A277935 A277936 * A277938 A277939 A277940

Keyword

nonn

Author

Chai Wah Wu, Mar 24 2017

Status

approved