A333767 Length of shortest run of zeros after a one in the binary expansion of n. a(0) = 0.

0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 4, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0

Offset: 0

Author

Gus Wiseman, Apr 06 2020

Keywords

• nonn

Examples

			The binary expansion of 148 is (1,0,0,1,0,1,0,0), so a(148) = 1.
		

Crossrefs

Positions of first appearances (ignoring index 0) are A000079.

Positions of terms > 0 are A022340.

Minimum prime index is A055396.

The maximum part minus 1 is given by A087117.

All of the following pertain to compositions in standard order (A066099):

- Length is A000120.

- Compositions without 1's are A022340.

- Sum is A070939.

- Product is A124758.

- Runs are counted by A124767.

- Strict compositions are A233564.

- Constant compositions are A272919.

- Runs-resistance is A333628.

- Maximum is A333766.

- Minimum is A333768.

- Weakly decreasing compositions are A114994.

- Weakly increasing compositions are A225620.

- Strictly decreasing compositions are A333255.

- Strictly increasing compositions are A333256.

Cf. A029931, A048793, A228351, A328594, A333217, A333218, A333219, A333632.

Programs

Mathematica

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Table[If[n==0,0,Min@@stc[n]-1],{n,0,100}]

Formula

For n > 0, a(n) = A333768(n) - 1.