A371572 Irregular triangle read by rows: row n lists the 1-based positions (starting from the left) of ones in the binary expansion of n, with row 0 = 0.

0, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 2, 3, 1, 1, 4, 1, 3, 1, 3, 4, 1, 2, 1, 2, 4, 1, 2, 3, 1, 2, 3, 4, 1, 1, 5, 1, 4, 1, 4, 5, 1, 3, 1, 3, 5, 1, 3, 4, 1, 3, 4, 5, 1, 2, 1, 2, 5, 1, 2, 4, 1, 2, 4, 5, 1, 2, 3, 1, 2, 3, 5, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 1, 6, 1, 5, 1, 5, 6

Offset

0,5

Links

Paolo Xausa, Table of n, a(n) for n = 0..11944 (rows 0..2200 of the triangle, flattened).

Michael De Vlieger, Plot (x,y) = (n,T(n,k)), n = 1..1024, where T(n,k) represents the k-th term in the n-th row of the irregular triangle, 32X vertical exaggeration.

Example

Triangle begins:
  [0] 0;
  [1] 1;
  [2] 1;
  [3] 1, 2;
  [4] 1;
  [5] 1, 3;
  [6] 1, 2;
  [7] 1, 2, 3;
  [8] 1;
  ...
Row n = 50 is 1, 2, 5:
  binary expansion of 50: 1 1 0 0 1 0
  positions of ones:      1 2 - - 5 -

Mathematica

Join[{{0}}, Array[Flatten[Position[IntegerDigits[#, 2], 1]] &, 50]]

Crossrefs

Cf. A230877 (row sums), A371571 (position of zeros).

Cf. A048793.

Sequence in context: A112377 A354521 A277760 * A127704 A307662 A050873

Adjacent sequences: A371569 A371570 A371571 * A371573 A371574 A371575

Keyword

nonn,base,tabf,easy

Author

Paolo Xausa, Mar 28 2024

Status

approved