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 A293405 The integer k that minimizes |k/n^2 - tau^2|, where tau = (1+sqrt(5))/2 (golden ratio). 3

%I #4 Oct 11 2017 21:57:05

%S 0,3,10,24,42,65,94,128,168,212,262,317,377,442,513,589,670,757,848,

%T 945,1047,1155,1267,1385,1508,1636,1770,1909,2053,2202,2356,2516,2681,

%U 2851,3026,3207,3393,3584,3780,3982,4189,4401,4618,4841,5069,5302,5540,5783

%N The integer k that minimizes |k/n^2 - tau^2|, where tau = (1+sqrt(5))/2 (golden ratio).

%H Clark Kimberling, <a href="/A293405/b293405.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = A293403(n) if (fractional part of (1+tau)*n^2) < 1/2, else a(n) = A293404(n).

%t z = 120; r = 1+GoldenRatio;

%t Table[Floor[r*n^2], {n, 0, z}]; (* A293403 *)

%t Table[Ceiling[r*n^2], {n, 0, z}]; (* A293404 *)

%t Table[Round[r*n^2], {n, 0, z}]; (* A293405 *)

%Y Cf. A001622, A293402, A293403, A293404.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Oct 11 2017

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Last modified July 19 16:24 EDT 2024. Contains 374410 sequences. (Running on oeis4.)