|
%I #18 Sep 08 2022 08:45:56
%S 1,4,7,10,12,15,18,20,22,25,28,31,33,36,38,41,43,46,49,52,54,57,59,62,
%T 64,67,70,73,75,77,80,83,85,88,91,94,96,98,101,104,106,109,112,115,
%U 116,119,122,125,127,130,133,136,137,140,143,146,148,151,154,156,158,161,164,167,169,172,175,177,179,182,185,188,190
%N a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sin(Pi/3), t=csc(Pi/3).
%C See A190006.
%H G. C. Greubel, <a href="/A190008/b190008.txt">Table of n, a(n) for n = 1..10000</a>
%F A190006: a(n) = n + [n*sin(Pi/3)] + [n*csc(Pi/3)].
%F A190007: b(n) = n + [n*csc(Pi/3)] + [n*(csc(Pi/3))^2].
%F A190008: c(n) = n + [n*sin(Pi/3)] + [n*(sin(Pi/3))^2].
%t r=1; s=Sin[Pi/3]; t=Csc[Pi/3];
%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}] (* A190006 *)
%t Table[b[n], {n, 1, 120}] (* A190007 *)
%t Table[c[n], {n, 1, 120}] (* A190008 *)
%o (Magma) C<i> := ComplexField(); [n + Floor(n*Sin(Pi(C)/3)) + Floor(n*(Sin(Pi(C)/3))^2): n in [1..100]]; // _G. C. Greubel_, Jan 11 2018
%Y Cf. A190006, A190007.
%K nonn
%O 1,2
%A _Clark Kimberling_, May 03 2011
|
