|
%I #9 Apr 11 2015 10:08:06
%S 1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6,1,2,3,4,5,6,7,8,1,2,3,4,5,
%T 6,7,8,1,9,2,3,4,5,6,7,8,1,9,2,10,3,4,5,6,7,8,1,9,2,10,3,11,4,5,6,7,8,
%U 1,9,2,10,3,11,4,12,5,6,7,8,1,9,2,10,3,11,4,12,5,13,6,7,8,1,9
%N Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=Pi.
%C See A194832 for a general discussion.
%e First nine rows:
%e 1
%e 1 2
%e 1 2 3
%e 1 2 3 4
%e 1 2 3 4 5
%e 1 2 3 4 5 6
%e 1 2 3 4 5 6 7
%e 8 1 2 3 4 5 6 7
%e 8 1 9 2 3 4 5 6 7
%t r = Pi;
%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}]] (* A194905 *)
%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}]] (* A194906 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n],
%t {n, 1, 80}]] (* A194907 *)
%Y Cf. A194832, A194906, A194907.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Sep 05 2011
|
