A189368 - OEIS

%I #14 Sep 08 2022 08:45:56

%S 3,6,10,13,18,21,24,28,32,36,39,42,46,50,54,57,61,65,68,72,75,79,83,

%T 86,90,93,98,101,105,108,111,116,119,123,126,130,134,137,141,144,148,

%U 152,155,159,163,167,170,173,178,181,185,188,191,196,199,203,206,211,214,217,221,224,229,232,235,239

%N a(n) = n + [n*r/s] + [n*t/s]; r=2, s=sqrt(2), t=sqrt(3).

%C See A189367.

%H G. C. Greubel, <a href="/A189368/b189368.txt">Table of n, a(n) for n = 1..10000</a>

%H Bernard J. Laurenzi, <a href="https://arxiv.org/abs/1901.03384">Special values of the Lommel functions and associated integrals</a>, arXiv:1901.03384 [math.CA], 2019.

%t r = 2; s = Sqrt[2]; t = Sqrt[3];

%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}]  (* A189367 *)

%t Table[g[n], {n, 1, 120}]  (* A189368 *)

%t Table[h[n], {n, 1, 120}]  (* A189369 *)

%o (PARI) for(n=1,100, print1(n + floor(2*n/sqrt(2)) + floor(n*sqrt(3)/sqrt(2)), ", ")) \\ _G. C. Greubel_, Apr 20 2018

%o (Magma) [n + Floor(2*n/Sqrt(2)) + Floor(n*Sqrt(3)/Sqrt(2)): n in [1..100]]; // _G. C. Greubel_, Apr 20 2018

%Y Cf. A189367, A189369.

%K nonn

%O 1,1

%A _Clark Kimberling_, Apr 20 2011