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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.

%I A359027 #29 Dec 15 2022 17:00:16
%S A359027 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,
%T A359027 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,
%U A359027 7,27,10,28,6,14,29,30,9,7,11,8,15,31,32,16,12,7,10
%N 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.
%C A359027 We write 1 into the first cell, then by leaving a gap of one empty cell we write another 1 into the third cell.
%C A359027 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.
%C A359027 It appears that the absolute values of A166711 appear in order nicely embedded into this sequence. - _Thomas Scheuerle_, Dec 12 2022
%H A359027 Thomas Scheuerle, <a href="/A359027/a359027.png">Scatter plot Y: ((1/2)+a(n))^(4/3) X: n = 1...20000</a>
%e A359027 Cell filling begins, starting from an empty line:
%e A359027   | | | | | | | | | | | | | | | | | | |
%e A359027   .
%e A359027   |1| |1| | | | | | | | | | | | | | | |
%e A359027   .
%e A359027   |1|2|1| | |2| | |2| | | | | | | | | |
%e A359027   .
%e A359027   |1|2|1|3| |2| | |2|3| | | |3| | | |3|
%o A359027 (MATLAB)
%o A359027 function a = A359027( max_n )
%o A359027     a = zeros(1,max_n);
%o A359027     f = 1:max_n; k = 1;
%o A359027     while ~isempty(f)
%o A359027         j = f(1:(k+1):end);
%o A359027         a(j(j(1:min(k+1,length(j))) <= max_n )) = k;
%o A359027         k = k+1;
%o A359027         f = find(a == 0);
%o A359027     end
%o A359027 end % _Thomas Scheuerle_, Dec 12 2022
%Y A359027 Cf. A166711.
%Y A359027 Cf. A028920 (with infinite copies).
%K A359027 nonn,easy
%O A359027 1,2
%A A359027 _Tamas Sandor Nagy_, Dec 12 2022