A385890 Positions of first appearances in A245563 = run lengths of binary indices.

1, 2, 4, 6, 8, 12, 14, 16, 22, 24, 28, 30, 32, 44, 46, 48, 54, 56, 60, 62, 64, 86, 88, 92, 94, 96, 108, 110, 112, 118, 120, 124, 126, 128, 172, 174, 176, 182, 184, 188, 190, 192, 214, 216, 220, 222, 224, 236, 238, 240, 246, 248, 252, 254, 256, 342, 344, 348

Offset: 1

Author

Gus Wiseman, Jul 18 2025

Keywords

• nonn

Comments

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.

Crossrefs

These are positions of firsts appearances in A245563, ranks A385889, reverse A245562.

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

A384877 lists anti-run lengths of binary indices, ranks A385816.

Cf. A000120, A023758, A048793, A069010, A200649, A243815, A246029, A328592, A384890.

Programs

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
q=Table[Length/@Split[bpe[n],#2==#1+1&],{n,0,1000}];
Select[Range[Length[q]-1],!MemberQ[Take[q,#-1],q[[#]]]&]