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A190000 a(n) = n + [n*r/s] + [n*t/s]; r=1, s=sinh(1), t=cosh(1).

%I A190000 #15 Sep 08 2022 08:45:56
%S A190000 2,5,8,12,15,18,21,24,27,31,34,37,41,43,46,50,53,56,59,63,65,68,72,75,
%T A190000 78,82,84,87,91,94,97,101,104,106,109,113,116,119,123,126,128,132,135,
%U A190000 138,142,145,147,151,154,157,160,164,167,169,173,176,179,183,186,189,192,195,198,202,205,208,211,214,217,220,224,227,230,233
%N A190000 a(n) = n + [n*r/s] + [n*t/s];  r=1, s=sinh(1), t=cosh(1).
%C A190000 See A189999.
%C A190000 Does the growth of a(n) oscillate with A020914(2*n-1), or does one sequence eventually outgrow the other? - _Jeffrey R. Goodwin_, Aug 26 2011
%H A190000 G. C. Greubel, <a href="/A190000/b190000.txt">Table of n, a(n) for n = 1..10000</a>
%F A190000 A189999:  a(n) = n + [n*sinh(1)] + [n*cosh(1)].
%F A190000 A190000:  b(n) = n + [n*csch(1)] + [n*coth(1)].
%F A190000 A190001:  c(n) = n + [n*sech(1)] + [n*tanh(1)].
%t A190000 r=1; s=Sinh[1]; t=Cosh[1];
%t A190000 a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t A190000 b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t A190000 c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t A190000 Table[a[n], {n, 1, 120}]  (* A189999 *)
%t A190000 Table[b[n], {n, 1, 120}]  (* A190000 *)
%t A190000 Table[c[n], {n, 1, 120}]  (* A190001 *)
%o A190000 (PARI) for(n=1,100, print1(n + floor(n/sinh(1)) + floor(n/tanh(1)), ", ")) \\ _G. C. Greubel_, Jan 11 2018
%o A190000 (Magma) [n + Floor(n/Sinh(1)) + Floor(n/Tanh(1)): n in [1..100]]; // _G. C. Greubel_, Jan 11 2018
%Y A190000 Cf. A189999, A190001.
%K A190000 nonn
%O A190000 1,1
%A A190000 _Clark Kimberling_, May 03 2011