A384890 - OEIS

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

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OFFSET

0,4

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?

LINKS

Table of n, a(n) for n=0..86.

EXAMPLE

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

MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

Table[Length[Split[bpe[n], #2!=#1+1&]], {n, 0, 100}]

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.

Sequence in context: A038374 A284569 A272604 * A284580 A227349 A246028

Adjacent sequences: A384887 A384888 A384889 * A384891 A384892 A384893

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 17 2025

STATUS

approved