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A194859 Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {e}, {2e}, ..., {ne}.

%I A194859 #5 Mar 30 2012 18:57:44
%S A194859 1,2,1,3,2,1,3,2,1,4,3,2,5,1,4,3,6,2,5,1,4,7,3,6,2,5,1,4,7,3,6,2,5,1,
%T A194859 8,4,7,3,6,2,9,5,1,8,4,7,3,10,6,2,9,5,1,8,4,7,3,10,6,2,9,5,1,8,4,11,7,
%U A194859 3,10,6,2,9,5,12,1,8,4,11,7,3,10,6,13,2,9,5,12,1,8,4,11,7,14,3
%N A194859 Triangular array (and fractal sequence):  row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {e}, {2e}, ..., {ne}.
%C A194859 See A194832 for a general discussion.
%e A194859 First nine rows:
%e A194859 1
%e A194859 2 1
%e A194859 3 2 1
%e A194859 3 2 1 4
%e A194859 3 2 5 1 4
%e A194859 3 6 2 5 1 4
%e A194859 7 3 6 2 5 1 4
%e A194859 7 3 6 2 5 1 8 4
%e A194859 7 3 6 2 9 5 1 8 4
%t A194859 r = E;
%t A194859 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194859 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194859 Sort[t[n], Less]], {n, 1, 20}]]  (* A194859 *)
%t A194859 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194859 Sort[t[n], Less]], {n, 1, 15}]]
%t A194859 row[n_] := Position[f, n];
%t A194859 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194859 g[n_, k_] := Part[row[n], k];
%t A194859 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194859 {k, 1, n}]]  (* A194860 *)
%t A194859 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194859 {n, 1, 80}]]  (* A194861 *)
%Y A194859 Cf. A194832, A194860, A194861.
%K A194859 nonn,tabl
%O A194859 1,2
%A A194859 _Clark Kimberling_, Sep 04 2011