A359027 A line of empty cells is filled by successive terms t >= 1 with t+1 copies of t and gaps of t empty cells between them.

1, 2, 1, 3, 4, 2, 5, 6, 2, 3, 7, 8, 4, 3, 9, 10, 5, 3, 11, 4, 12, 6, 13, 14, 4, 5, 7, 15, 16, 4, 8, 6, 5, 17, 18, 9, 19, 7, 5, 20, 6, 10, 21, 22, 5, 8, 11, 23, 6, 7, 24, 12, 9, 25, 26, 6, 13, 8, 7, 27, 10, 28, 6, 14, 29, 30, 9, 7, 11, 8, 15, 31, 32, 16, 12, 7, 10

Offset: 1

Author

Tamas Sandor Nagy, Dec 12 2022

Keywords

• nonn
• easy

Comments

We write 1 into the first cell, then by leaving a gap of one empty cell we write another 1 into the third cell.

Next, we write 2 into the first available empty cell, then write two more 2's by leaving gaps of two empty cells between them. And so on.

It appears that the absolute values of A166711 appear in order nicely embedded into this sequence. - Thomas Scheuerle, Dec 12 2022

Examples

			Cell filling begins, starting from an empty line:
  | | | | | | | | | | | | | | | | | | |
  .
  |1| |1| | | | | | | | | | | | | | | |
  .
  |1|2|1| | |2| | |2| | | | | | | | | |
  .
  |1|2|1|3| |2| | |2|3| | | |3| | | |3|
		

Links

• Thomas Scheuerle, Scatter plot Y: ((1/2)+a(n))^(4/3) X: n = 1...20000

Crossrefs

Cf. A166711.

Cf. A028920 (with infinite copies).

Programs

MATLAB

function a = A359027( max_n )
    a = zeros(1,max_n);
    f = 1:max_n; k = 1;
    while ~isempty(f)
        j = f(1:(k+1):end);
        a(j(j(1:min(k+1,length(j))) <= max_n )) = k;
        k = k+1;
        f = find(a == 0);
    end
end % Thomas Scheuerle, Dec 12 2022