A384890 Number of maximal anti-runs (increasing by more than 1) in the binary indices of n.

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

Offset: 0

Author

Gus Wiseman, Jun 17 2025

Keywords

• nonn

Comments

First differs from A272604 at a(51) = 3, A272604(51) = 2.

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

Do all constant runs in this sequence have lengths 1, 2, or 3?

Examples

			The binary indices of 51 are {1,2,5,6}, with maximal anti-runs ((1),(2,5),(6)), so a(51) = 3.
		

Crossrefs

For runs instead of anti-runs we have A069010 = run-lengths of A245563 (reverse A245562).

Row-lengths of A384877, firsts A384878.

For prime indices instead of binary indices we have A384906.

A000120 counts binary indices.

A356606 counts strict partitions without a neighborless part, complement A356607.

A384175 counts subsets with all distinct lengths of maximal runs, complement A384176.

Cf. A044813, A048793, A052499, A164707, A243815, A300820, A328592, A384177, A384879, A384893.

Programs

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
Table[Length[Split[bpe[n],#2!=#1+1&]],{n,0,100}]