A190086 - OEIS

%I #18 Sep 08 2022 08:45:56

%S 4,9,14,19,24,28,33,38,43,48,53,58,63,68,73,78,83,87,92,97,102,107,

%T 112,117,122,127,132,137,142,146,151,156,161,166,172,176,181,186,191,

%U 196,201,205,210,215,220,225,231,235,240,245,250,255,260,264,269,274,279,284,289,294,299,304,309,314,318,323,328,333,338,344,348

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

%C See A190085.

%H G. C. Greubel, <a href="/A190086/b190086.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)], this sequence.

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

%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/sin(1/2)) + floor(n/tan(1/2)), ", ")) \\ _G. C. Greubel_, Mar 04 2018

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

%Y Cf. A190085, A190087.

%K nonn

%O 1,1

%A _Clark Kimberling_, May 04 2011