cp's OEIS Frontend

A191453 Dispersion of (2*floor(3*n/2)), by antidiagonals.

%I A191453 #12 Oct 21 2024 00:55:33
%S A191453 1,2,3,6,8,4,18,24,12,5,54,72,36,14,7,162,216,108,42,20,9,486,648,324,
%T A191453 126,60,26,10,1458,1944,972,378,180,78,30,11,4374,5832,2916,1134,540,
%U A191453 234,90,32,13,13122,17496,8748,3402,1620,702,270,96,38,15,39366
%N A191453 Dispersion of (2*floor(3*n/2)), by antidiagonals.
%C A191453 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 A191453 (1) s=A000040 (the primes), D=A114537, u=A114538.
%C A191453 (2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
%C A191453 (3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
%C A191453 More recent examples of dispersions: A191426-A191455.
%e A191453 Northwest corner:
%e A191453   1...2....6....18...54
%e A191453   3...8....24...72...216
%e A191453   4...12...36...108..324
%e A191453   5...14...42...126..378
%e A191453   7...20...60...180..540
%t A191453 (* Program generates the dispersion array T of increasing sequence f[n] *)
%t A191453 r=40; r1=12; c=40; c1=12;
%t A191453 f[n_] :=2Floor[3n/2]   (* complement of column 1 *)
%t A191453 mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
%t A191453 rows = {NestList[f, 1, c]};
%t A191453 Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
%t A191453 t[i_, j_] := rows[[i, j]];
%t A191453 TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
%t A191453 (* A191453 array *)
%t A191453 Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191453 sequence *)
%t A191453 (* Program by _Peter J. C. Moses_, Jun 01 2011 *)
%Y A191453 Cf. A114537, A035513, A035506.
%K A191453 nonn,tabl
%O A191453 1,2
%A A191453 _Clark Kimberling_, Jun 05 2011