A190087 - OEIS

%I #17 Sep 08 2022 08:45:56

%S 2,5,7,10,12,15,17,21,23,26,29,31,34,36,40,42,45,47,50,52,55,59,61,64,

%T 66,69,71,74,77,80,82,85,88,90,93,96,99,101,104,106,109,111,114,118,

%U 120,123,125,128,130,133,136,139,141,144,147,149,152,155,158,160,163,165,168,170,174,177,179,182,184,187,189,193,195,198,200

%N a(n) = n + [n*r/t] + [n*s/t];  r=1, s=sin(1/2), t=cos(1/2).

%C See A190085.

%H G. C. Greubel, <a href="/A190087/b190087.txt">Table of n, a(n) for n = 1..10000</a>

%F A190085:  f(n) = n + [n*sin(1/2)] + [n*cos(1/2)].

%F A190086:  g(n) = n + [n*csc(1/2)] + [n*cot(1/2)].

%F A190087:  h(n) = n + [n*sec(1/2)] + [n*tan(1/2)], this sequence.

%t r=1; s=Sin[1/2]; t=Cos[1/2];

%t f[n_] := n + Floor[n*s/r] + Floor[n*t/r];

%t g[n_] := n + Floor[n*r/s] + Floor[n*t/s];

%t h[n_] := n + Floor[n*r/t] + Floor[n*s/t];

%t Table[f[n], {n, 1, 120}]  (* A190085 *)

%t Table[g[n], {n, 1, 120}]  (* A190086 *)

%t Table[h[n], {n, 1, 120}]  (* A190087 *)

%o (PARI) for(n=1,100, print1(n + floor(n/cos(1/2)) + floor(n*tan(1/2)), ", ")) \\ _G. C. Greubel_, Mar 04 2018

%o (Magma) [n + Floor(n/Cos(1/2)) + Floor(n*Tan(1/2)): n in [1..100]]; // _G. C. Greubel_, Mar 04 2018

%Y Cf. A190085, A190086.

%K nonn

%O 1,1

%A _Clark Kimberling_, May 04 2011