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Least integer k such that k/n^2 > (1 + sqrt(5))/2 (the golden ratio).
5

%I #4 Oct 11 2017 18:14:45

%S 0,2,7,15,26,41,59,80,104,132,162,196,233,274,318,365,415,468,525,585,

%T 648,714,784,856,932,1012,1094,1180,1269,1361,1457,1555,1657,1763,

%U 1871,1983,2097,2216,2337,2462,2589

%N Least integer k such that k/n^2 > (1 + sqrt(5))/2 (the golden ratio).

%H Clark Kimberling, <a href="/A293401/b293401.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = ceiling(r*n^2), where r = (1 + sqrt(5))/2.

%F a(n) = A293400(n) + 1 for n > 0.

%t z = 120; r = GoldenRatio;

%t Table[Floor[r*n^2], {n, 0, z}]; (* A293400 *)

%t Table[Ceiling[r*n^2], {n, 0, z}]; (* A293401 *)

%t Table[Round[r*n^2], {n, 0, z}]; (* A293402 *)

%Y Cf. A001622, A293400, A293402.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Oct 11 2017