A385892 In the sequence of run lengths of binary indices of each positive integer (A245563), remove all duplicate rows after the first and take the last term of each remaining row.

1, 2, 1, 3, 1, 2, 4, 1, 1, 2, 3, 5, 1, 1, 1, 2, 2, 3, 4, 6, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 7, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7

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.

Examples

			The binary indices of 53 are {1,3,5,6}, with maximal runs ((1),(3),(5,6)), with lengths (1,1,2), which is the 16th row of A385817, so a(16) = 2.
		

Crossrefs

In the following references, "before" is short for "before removing duplicate rows".

Positions of firsts appearances appear to be A000071.

Without the removals we have A090996.

For sum instead of last we have A200648, before A000120.

For length instead of last we have A200650+1, before A069010 = A037800+1.

Last term of row n of A385817 (ranks A385818, before A385889), first A083368.

A245563 gives run lengths of binary indices, see A245562, A246029, A328592.

A384877 gives anti-run lengths of binary indices, A385816.

Cf. A001629, A044813, A048793, A164707, A200649, A384878, A384890, A385886.

Programs

Mathematica

Last/@DeleteDuplicates[Table[Length/@Split[Join@@Position[Reverse[IntegerDigits[n,2]],1],#2==#1+1&],{n,100}]]