|
%I #9 Sep 08 2022 08:45:56
%S 2,5,8,11,14,17,20,23,26,28,31,34,37,40,43,46,49,52,54,57,60,63,66,69,
%T 72,75,78,81,83,86,89,92,95,98,101,104,107,109,112,115,118,121,124,
%U 127,130,133,136,138,141,144,147,150,153,156,159,162,164,167,170,173,176,179,182,185,188,191,193,196,199,202,205,208,211,214,217
%N a(n) = A189932(n)/2.
%C See A189932.
%H G. C. Greubel, <a href="/A189934/b189934.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals (n + floor(n*(csc(pi/5))^2) + floor(n*(cot(pi/5))^2))/2, for n>=1. - _G. C. Greubel_, Jan 13 2018
%t r=1; s=Sin[Pi/5]^2; t=Cos[Pi/5]^2;
%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}] (*A005408*)
%t Table[b[n], {n, 1, 120}] (*A189932*)
%t Table[c[n], {n, 1, 120}] (*A189933*)
%t Table[b[n]/2, {n, 1, 120}] (*A189934*)
%t Table[c[n]/2, {n, 1, 120}] (*A189935*)
%o (PARI) for(n=1,100, print1((n + floor(n/(sin(Pi/5))^2) + floor(n/(tan(Pi/5))^2))/2, ", ")) \\ _G. C. Greubel_, Jan 13 2018
%o (Magma) C<i> := ComplexField(); [(n + Floor(n/(Sin(Pi(C)/5))^2) + Floor(n/(Tan(Pi(C)/5))^2))/2: n in [1..100]]; // _G. C. Greubel_, Jan 13 2018
%Y Cf. A189932, A189933, A189935.
%K nonn
%O 1,1
%A _Clark Kimberling_, May 01 2011
|
