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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}. 4

%I

%S 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 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 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 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 See A194832 for a general discussion.

%e First nine rows:

%e 1

%e 2 1

%e 3 2 1

%e 3 2 1 4

%e 3 2 5 1 4

%e 3 6 2 5 1 4

%e 7 3 6 2 5 1 4

%e 7 3 6 2 5 1 8 4

%e 7 3 6 2 9 5 1 8 4

%t r = E;

%t t[n_] := Table[FractionalPart[k*r], {k, 1, n}];

%t f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@

%t Sort[t[n], Less]], {n, 1, 20}]] (* A194859 *)

%t TableForm[Table[Flatten[(Position[t[n], #1] &) /@

%t Sort[t[n], Less]], {n, 1, 15}]]

%t row[n_] := Position[f, n];

%t u = TableForm[Table[row[n], {n, 1, 20}]]

%t g[n_, k_] := Part[row[n], k];

%t p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},

%t {k, 1, n}]] (* A194860 *)

%t q[n_] := Position[p, n]; Flatten[Table[q[n],

%t {n, 1, 80}]] (* A194861 *)

%Y Cf. A194832, A194860, A194861.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 04 2011

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Last modified August 5 11:15 EDT 2021. Contains 346467 sequences. (Running on oeis4.)