|
%I #13 Sep 08 2022 08:45:57
%S 1,3,5,7,9,12,14,16,18,20,23,25,26,28,30,33,35,37,39,41,44,46,48,50,
%T 51,54,56,58,60,62,65,67,69,71,73,76,77,79,81,83,86,88,90,92,94,97,99,
%U 101,102,104,107,109,111,113,115,118,120,122,124,126,128,130,132,134,136,139,141,143,145,147,150,152,153,155,157,160
%N a(n) = n + [n*r/t] + [n*s/t]; r=1/2, s=sinh(Pi/2), t=cosh(Pi/2).
%C See A190326.
%H G. C. Greubel, <a href="/A190328/b190328.txt">Table of n, a(n) for n = 1..10000</a>
%F A190326: f(n) = n + [2*n*sinh(Pi/2)] + [2*n*cosh(Pi/2)].
%F A190327: g(n) = n + [n*csch(Pi/2)/2] + [n*coth(Pi/2)].
%F A190328: h(n) = n + [n*sech(Pi/2)/2] + [n*tanh(Pi/2)].
%p r:=1/2: s:=sinh(Pi/2): t:=cosh(Pi/2): seq(n+floor(n*r/t)+floor(n*s/t),n=1..80); # _Muniru A Asiru_, Apr 05 2018
%t r=1/2; s=Sinh[Pi/2]; t=Cosh[Pi/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}] (* A190326 *)
%t Table[g[n], {n, 1, 120}] (* A190327 *)
%t Table[h[n], {n, 1, 120}] (* A190328 *)
%o (PARI) for(n=1,100, print1(n + floor(n/(2*cosh(Pi/2))) + floor(n*tanh(Pi/2)), ", ")) \\ _G. C. Greubel_, Apr 04 2018
%o (Magma) R:=RealField(); [n + Floor(n/(2*Cosh(Pi(R)/2))) + Floor(n*Tanh(Pi(R)/2)): n in [1..100]]; // _G. C. Greubel_, Apr 04 2018
%Y Cf. A190326, A190327.
%K nonn
%O 1,2
%A _Clark Kimberling_, May 08 2011
|
