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A191545 Dispersion of (floor(9*n/4)), by antidiagonals.

%I A191545 #14 Jun 12 2025 21:39:24
%S A191545 1,2,3,4,6,5,9,13,11,7,20,29,24,15,8,45,65,54,33,18,10,101,146,121,74,
%T A191545 40,22,12,227,328,272,166,90,49,27,14,510,738,612,373,202,110,60,31,
%U A191545 16,1147,1660,1377,839,454,247,135,69,36,17,2580,3735,3098,1887
%N A191545 Dispersion of (floor(9*n/4)), by antidiagonals.
%C A191545 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 A191545 (1) s=A000040 (the primes), D=A114537, u=A114538.
%C A191545 (2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
%C A191545 (3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
%C A191545 More recent examples of dispersions: A191426-A191455.
%e A191545 Northwest corner:
%e A191545   1   2    4    9    20
%e A191545   3   6    13   29   65
%e A191545   5   11   25   54   121
%e A191545   7   15   33   74   166
%e A191545   8   18   40   90   202
%t A191545 (* Program generates the dispersion array T of the complement of increasing sequence f[n] *)
%t A191545 r=40; r1=12; c=40; c1=12; f[n_] := Floor[9n/4]   (* complement of column 1 *)
%t A191545 mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
%t A191545 rows = {NestList[f, 1, c]};
%t A191545 Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
%t A191545 t[i_, j_] := rows[[i, j]];
%t A191545 TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
%t A191545 (* A191545 array *)
%t A191545 Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191545 sequence *)
%t A191545 (* Program by _Peter J. C. Moses_, Jun 01 2011 *)
%Y A191545 Cf. A114537, A035513, A035506.
%K A191545 nonn,tabl
%O A191545 1,2
%A A191545 _Clark Kimberling_, Jun 09 2011