A189467 - OEIS

%I #15 Sep 08 2022 08:45:56

%S 1,3,6,8,10,12,14,17,19,21,23,25,28,30,32,34,37,39,41,43,45,48,50,52,

%T 54,56,59,61,63,65,67,70,72,74,76,78,81,83,85,87,89,92,94,96,98,101,

%U 103,105,107,109,112,114,116,118,120,123,125,127,129,131,134,136,138,140,142,145,147,149,151,153,156,158,160,162,165,167,169,171,173,176,178,180,182,184

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

%C See A189459.

%H Ivan Panchenko, <a href="/A189467/b189467.txt">Table of n, a(n) for n = 1..10000</a>

%t r=1; s=1+2^(1/2); t=1/2+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}]  (* A189459 *)

%t Table[g[n], {n, 1, 120}]  (* A189467 *)

%t Table[h[n], {n, 1, 120}]  (* A189468 *)

%o (PARI) for(n=1,100, print1(n + floor(n/(1 + sqrt(2))) + floor(n*(1+2*sqrt(2))/(2+2*sqrt(2))), ", ")) \\ _G. C. Greubel_, Apr 13 2018

%o (Magma) [n + Floor(n/(1 + Sqrt(2))) + Floor(n*(1+2*Sqrt(2))/(2 + 2*Sqrt(2))) : n in [1..100]]; // _G. C. Greubel_, Apr 13 2018

%Y Cf. A189459, A189468.

%K nonn

%O 1,2

%A _Clark Kimberling_, Apr 22 2011