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A293504 The integer k that minimizes |k/n^2 - sqrt(2)|. 3

%I #8 Sep 08 2022 08:46:20

%S 0,1,6,13,23,35,51,69,91,115,141,171,204,239,277,318,362,409,458,511,

%T 566,624,684,748,815,884,956,1031,1109,1189,1273,1359,1448,1540,1635,

%U 1732,1833,1936,2042,2151,2263,2377,2495,2615,2738,2864,2992,3124,3258

%N The integer k that minimizes |k/n^2 - sqrt(2)|.

%H Clark Kimberling, <a href="/A293504/b293504.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor(1/2 + (n^2)*sqrt(2)).

%F a(n) = A293502(n) if (fractional part of (sqrt(2))*n^2) < 1/2, else a(n) = A293503(n).

%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--; round(n^2*sqrt(2))) \\ _G. C. Greubel_, Aug 16 2018

%o (Magma) [Round(n^2*Sqrt(2)): n in [0..100]]; // _G. C. Greubel_, Aug 16 2018

%Y Cf. A002193, A293502, A293503.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Oct 12 2017

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Last modified April 21 01:36 EDT 2024. Contains 371850 sequences. (Running on oeis4.)