A333766 Maximum part of the n-th composition in standard order. a(0) = 0.

0, 1, 2, 1, 3, 2, 2, 1, 4, 3, 2, 2, 3, 2, 2, 1, 5, 4, 3, 3, 3, 2, 2, 2, 4, 3, 2, 2, 3, 2, 2, 1, 6, 5, 4, 4, 3, 3, 3, 3, 4, 3, 2, 2, 3, 2, 2, 2, 5, 4, 3, 3, 3, 2, 2, 2, 4, 3, 2, 2, 3, 2, 2, 1, 7, 6, 5, 5, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 5, 4, 3, 3, 3, 2, 2

Offset: 0

Author

Gus Wiseman, Apr 05 2020

Keywords

• nonn

Comments

One plus the longest run of 0's in the binary expansion of n.

A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (row k of A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

Examples

			The 100th composition in standard order is (1,3,3), so a(100) = 3.
		

Crossrefs

Positions of ones are A000225.

Positions of terms <= 2 are A003754.

The version for prime indices is A061395.

Positions of terms > 1 are A062289.

Positions of first appearances are A131577.

The minimum part is given by A333768.

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.

- Weakly decreasing compositions are A114994.

- Weakly increasing compositions are A225620.

- Strictly decreasing compositions are A333255.

- Strictly increasing compositions are A333256.

Cf. A029931, A048793, A087117, A228351, A328594, A333217, A333218, A333219, A333632, A333767.

Programs

Mathematica

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

Formula

For n > 0, a(n) = A087117(n) + 1.