cp's OEIS Frontend

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

%I A384890 #9 Jun 18 2025 07:35:38
%S A384890 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,
%T A384890 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,
%U A384890 1,1,2,3,1,1,1,2,2,2,3,4,1,1,1,2,1,1,2
%N A384890 Number of maximal anti-runs (increasing by more than 1) in the binary indices of n.
%C A384890 First differs from A272604 at a(51) = 3, A272604(51) = 2.
%C A384890 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.
%C A384890 Do all constant runs in this sequence have lengths 1, 2, or 3?
%e A384890 The binary indices of 51 are {1,2,5,6}, with maximal anti-runs ((1),(2,5),(6)), so a(51) = 3.
%t A384890 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A384890 Table[Length[Split[bpe[n],#2!=#1+1&]],{n,0,100}]
%Y A384890 For runs instead of anti-runs we have A069010 = run-lengths of A245563 (reverse A245562).
%Y A384890 Row-lengths of A384877, firsts A384878.
%Y A384890 For prime indices instead of binary indices we have A384906.
%Y A384890 A000120 counts binary indices.
%Y A384890 A356606 counts strict partitions without a neighborless part, complement A356607.
%Y A384890 A384175 counts subsets with all distinct lengths of maximal runs, complement A384176.
%Y A384890 Cf. A044813, A048793, A052499, A164707, A243815, A300820, A328592, A384177, A384879, A384893.
%K A384890 nonn
%O A384890 0,4
%A A384890 _Gus Wiseman_, Jun 17 2025