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Greatest integer k such that k/n^2 < sqrt(2).
3

%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