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

1,2

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

Links

Table of n, a(n) for n=1..77.

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

Example

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

Prog

(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

Crossrefs

Cf. A166711.

Cf. A028920 (with infinite copies).

Sequence in context: A117384 A358799 A125160 * A366691 A009947 A166711

Adjacent sequences: A359024 A359025 A359026 * A359028 A359029 A359030

Keyword

nonn,easy

Author

Tamas Sandor Nagy, Dec 12 2022

Status

approved