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

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

%S 1,3,5,8,10,12,14,15,17,19,22,24,26,27,29,31,34,36,38,39,41,43,46,48,

%T 50,51,53,55,57,60,62,64,65,67,69,72,74,76,77,79,81,84,86,88,89,91,93,

%U 96,98,100,102,103,105,107,110,112,114,115,117,119,122,124,126

%N Position of 2n+cos(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. A206910.

%K nonn

%O 1,2

%A _Clark Kimberling_, Feb 13 2012