%I #9 Sep 08 2022 08:46:19
%S 0,1,5,12,22,35,50,69,90,114,141,171,203,239,277,318,362,408,458,510,
%T 565,623,684,748,814,883,956,1030,1108,1189,1272,1359,1448,1540,1634,
%U 1732,1832,1936,2042,2151,2262,2377,2494,2614,2737,2863,2992,3123,3258
%N Greatest integer k such that k/n^2 < sqrt(2).
%H Clark Kimberling, <a href="/A293502/b293502.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = floor(r*n^2), where r = sqrt(2).
%F a(n) = A293503(n) - 1 for n > 0.
%t z = 120; r = Sqrt[2];
%t Table[Floor[r*n^2], {n, 0, z}]; (* A293502 *)
%t Table[Ceiling[r*n^2], {n, 0, z}]; (* A293503 *)
%t Table[Round[r*n^2], {n, 0, z}]; (* A293504 *)
%o (PARI) vector(100, n, n--; floor(n^2*sqrt(2))) \\ _G. C. Greubel_, Aug 16 2018
%o (Magma) [Floor(n^2*Sqrt(2)): n in [0..100]]; // _G. C. Greubel_, Aug 16 2018
%Y Cf. A002193, A293503, A293504.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Oct 11 2017