A372515 Irregular triangle read by rows where row n lists the positions of zeros in the reversed binary expansion of n.

1, 1, 2, 2, 1, 1, 2, 3, 2, 3, 1, 3, 3, 1, 2, 2, 1, 1, 2, 3, 4, 2, 3, 4, 1, 3, 4, 3, 4, 1, 2, 4, 2, 4, 1, 4, 4, 1, 2, 3, 2, 3, 1, 3, 3, 1, 2, 2, 1, 1, 2, 3, 4, 5, 2, 3, 4, 5, 1, 3, 4, 5, 3, 4, 5, 1, 2, 4, 5, 2, 4, 5, 1, 4, 5, 4, 5, 1, 2, 3, 5, 2, 3, 5, 1, 3, 5

Offset: 1

Author

Gus Wiseman, May 26 2024

Keywords

• nonn
• base
• tabf

Examples

			The reversed binary expansion of 100 is (0,0,1,0,0,1,1), with zeros at positions {1,2,4,5}, so row 100 is (1,2,4,5).
Triangle begins:
   1:
   2: 1
   3:
   4: 1 2
   5: 2
   6: 1
   7:
   8: 1 2 3
   9: 2 3
  10: 1 3
  11: 3
  12: 1 2
  13: 2
  14: 1
  15:
  16: 1 2 3 4
		

Crossrefs

Row lengths are A023416, partial sums A059015.

For ones instead of zeros we have A048793, lengths A000120, sums A029931.

Row sums are A359400, non-reversed A359359.

Same as A368494 but with empty rows () instead of (0).

A003714 lists numbers with no successive binary indices.

A030190 gives binary expansion, reverse A030308.

A039004 lists the positions of zeros in A345927.

Cf. A069010, A070939, A073642, A230877, A344618, A359402, A359495.

Programs

Mathematica

Table[Join@@Position[Reverse[IntegerDigits[n,2]],0],{n,30}]