cp's OEIS Frontend

A191541 Dispersion of (2*floor(n*sqrt(2))), by antidiagonals.

%I A191541 #11 Oct 21 2024 01:20:14
%S A191541 1,2,3,4,8,5,10,22,14,6,28,62,38,16,7,78,174,106,44,18,9,220,492,298,
%T A191541 124,50,24,11,622,1390,842,350,140,66,30,12,1758,3930,2380,988,394,
%U A191541 186,84,32,13,4972,11114,6730,2794,1114,526,236,90,36,15,14062,31434
%N A191541 Dispersion of (2*floor(n*sqrt(2))), by antidiagonals.
%C A191541 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 A191541 (1) s=A000040 (the primes), D=A114537, u=A114538.
%C A191541 (2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
%C A191541 (3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
%C A191541 More recent examples of dispersions: A191426-A191455.
%e A191541 Northwest corner:
%e A191541   1...2....4....10...28
%e A191541   3...8....22...62...174
%e A191541   5...14...38...106..298
%e A191541   6...16...44...124..350
%e A191541   7...18...50...140..394
%t A191541 (* Program generates the dispersion array T of the complement of increasing sequence f[n] *)
%t A191541 r=40; r1=12; c=40; c1=12; f[n_] :=2*Floor[n*Sqrt[2]]   (* complement of column 1 *)
%t A191541 mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
%t A191541 rows = {NestList[f, 1, c]};
%t A191541 Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
%t A191541 t[i_, j_] := rows[[i, j]];
%t A191541 TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
%t A191541 (* A191541 array *)
%t A191541 Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191541 sequence *)
%t A191541 (* Program by _Peter J. C. Moses_, Jun 01 2011 *)
%Y A191541 Cf. A114537, A035513, A035506, A191540.
%K A191541 nonn,tabl
%O A191541 1,2
%A A191541 _Clark Kimberling_, Jun 07 2011