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Position of 2n+sin(n) when the sets {2k+cos(k)} and {2k+sin(k)} are jointly ranked.
2

%I #5 Mar 30 2012 18:58:12

%S 2,4,6,7,9,11,13,16,18,20,21,23,25,28,30,32,33,35,37,40,42,44,45,47,

%T 49,52,54,56,58,59,61,63,66,68,70,71,73,75,78,80,82,83,85,87,90,92,94,

%U 95,97,99,101,104,106,108,109,111,113,116,118,120,121,123,125

%N Position of 2n+sin(n) when the sets {2k+cos(k)} and {2k+sin(k)} are jointly ranked.

%t f[n_] := N[2 n + Cos[n]];

%t g[n_] := N[2 n + Sin[n]]; z = 120;

%t c = Table[f[n], {n, 1, z}];

%t s = Table[g[n], {n, 1, z}];

%t j = Sort[Union[c, s]];

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

%t q[n_] := Position[j, g[n]];

%t Flatten[Table[p[n], {n, 1, z}]] (* A206909 *)

%t Flatten[Table[q[n], {n, 1, z}]] (* A206910 *)

%Y Cf. A206909.

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 13 2012