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%I #8 Dec 09 2017 20:07:55
%S 1,3,2,9,6,4,25,17,12,5,70,47,34,14,7,194,130,94,39,20,8,537,360,260,
%T 108,56,23,10,1485,996,719,299,155,64,28,11,4105,2753,1988,827,429,
%U 177,78,31,13,11346,7610,5495,2286,1186,490,216,86,36,15,31360,21034
%N Dispersion of (5n-floor(n*sqrt(5))), by antidiagonals.
%C 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 (1) s=A000040 (the primes), D=A114537, u=A114538.
%C (2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
%C (3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
%C More recent examples of dispersions: A191426-A191455 and A191536-A191545.
%H G. C. Greubel, <a href="/A191539/b191539.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%e Northwest corner:
%e 1...3....9....25...70
%e 2...6....17...47...130
%e 4...12...34...94...260
%e 5...14...39..108...299
%e 7...20...56...155..429
%t (* Program generates the dispersion array T of the increasing sequence f[n] *)
%t r=40; r1=12; c=40; c1=12; f[n_] :=5n-Floor[n*Sqrt[5]] (* complement of column 1 *)
%t mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
%t rows = {NestList[f, 1, c]};
%t Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
%t t[i_, j_] := rows[[i, j]];
%t TableForm[Table[t[i, j], {i, 1, r1}, {j, 1, c1}]] (* A191539 array *)
%t Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191539 sequence *)
%Y Cf. A114537, A035513, A035506.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Jun 06 2011
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