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%I #14 Sep 08 2022 08:45:56
%S 3,7,12,15,19,24,27,32,36,40,44,48,52,56,60,65,68,72,77,81,84,89,93,
%T 97,101,105,109,113,117,122,125,130,134,137,142,146,149,154,158,163,
%U 166,170,175,178,182,187,190,195,199,203,207,211,215,219,223,228
%N b(n) = n + [n*r/s] + [n*t/s]; r=1, s=sin(Pi/5), t=cos(Pi/5), where [] denotes the floor function.
%H G. C. Greubel, <a href="/A189927/b189927.txt">Table of n, a(n) for n = 1..10000</a>
%F A189926: a(n) = n + [n*sin(pi/5)] + [n*cos(Pi/5)].
%F A189927: b(n) = n + [n*csc(pi/5)] + [n*cot(Pi/5)].
%F A189928: c(n) = n + [n*sec(pi/5)] + [n*tan(Pi/5)].
%t r=1; s=Sin[Pi/5]; t=Cos[Pi/5];
%t a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t Table[a[n], {n, 1, 120}] (* A189926 *)
%t Table[b[n], {n, 1, 120}] (* A189927 *)
%t Table[c[n], {n, 1, 120}] (* A189928 *)
%o (PARI) for(n=1,100, print1(n + floor(n/sin(Pi/5)) + floor(n/tan(Pi/5)), ", ")) \\ _G. C. Greubel_, Jan 13 2018
%o (Magma) C<i> := ComplexField(); [n + Floor(n/Sin(Pi(C)/5)) + Floor(n/Tan(Pi(C)/5)): n in [1..100]]; // _G. C. Greubel_, Jan 13 2018
%Y Cf. A189926, A189928.
%K nonn
%O 1,1
%A _Clark Kimberling_, May 01 2011
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