cp's OEIS Frontend

A191543 Dispersion of (floor(8*n/3)), by antidiagonals.

%I A191543 #14 Jun 12 2025 21:21:47
%S A191543 1,2,3,5,8,4,13,21,10,6,34,56,26,16,7,90,149,69,42,18,9,240,397,184,
%T A191543 112,48,24,11,640,1058,490,298,128,64,29,12,1706,2821,1306,794,341,
%U A191543 170,77,32,14,4549,7522,3482,2117,909,453,205,85,37,15,12130,20058
%N A191543 Dispersion of (floor(8*n/3)), by antidiagonals.
%C A191543 Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
%C A191543 (1) s=A000040 (the primes), D=A114537, u=A114538.
%C A191543 (2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
%C A191543 (3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
%C A191543 More recent examples of dispersions: A191426-A191455.
%e A191543 Northwest corner:
%e A191543   1   2    5    13   34
%e A191543   3   8    21   56   149
%e A191543   4   10   26   69   184
%e A191543   6   16   42   112  298
%e A191543   7   18   48   128  341
%t A191543 (* Program generates the dispersion array T of the complement of increasing sequence f[n] *)
%t A191543 r=40; r1=12; c=40; c1=12; f[n_] := Floor[8n/3]   (* complement of column 1 *)
%t A191543 mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
%t A191543 rows = {NestList[f, 1, c]};
%t A191543 Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
%t A191543 t[i_, j_] := rows[[i, j]];
%t A191543 TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
%t A191543 (* A191543 array *)
%t A191543 Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191543 sequence *)
%t A191543 (* Program by _Peter J. C. Moses_, Jun 01 2011 *)
%Y A191543 Cf. A114537, A035513, A035506.
%K A191543 nonn,tabl
%O A191543 1,2
%A A191543 _Clark Kimberling_, Jun 07 2011