A189382 - OEIS

%I #9 Sep 08 2022 08:45:56

%S 1,2,4,5,7,9,10,12,13,15,16,18,20,21,23,24,26,28,29,31,32,34,35,37,39,

%T 40,42,43,45,47,48,50,51,53,55,56,58,59,61,62,64,66,67,69,70,72,74,75,

%U 77,78,80,81,83,85,86,88,89,91,93,94,96,97,99,100,102,104,105,107,108,110,112,113,115,116,118,120,121,123,124,126,127,129,131,132,134

%N a(n) = n + [n*r/t] + [n*s/t]; r=1, s=-1+sqrt(2), t=1+sqrt(2).

%C See A189380.

%H G. C. Greubel, <a href="/A189382/b189382.txt">Table of n, a(n) for n = 1..10000</a>

%t r=1; s=-1+2^(1/2); t=1+2^(1/2);

%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}]  (* A189380 *)

%t Table[g[n], {n, 1, 120}]  (* A189381 *)

%t Table[h[n], {n, 1, 120}]  (* A189382 *)

%o (PARI) for(n=1, 100, print1(n + floor(n/(sqrt(2)+1)) + floor(n*(sqrt(2)-1)/(sqrt(2)+1)), ", ")) \\ _G. C. Greubel_, Apr 20 2018

%o (Magma) [n + Floor(n/(Sqrt(2)+1)) + Floor(n*(Sqrt(2)-1)/(Sqrt(2)+1)): n in [1..100]]; // _G. C. Greubel_, Apr 20 2018

%Y Cf. A189380, A189381.

%K nonn

%O 1,2

%A _Clark Kimberling_, Apr 20 2011