A293402 The integer k that minimizes |k/n^2 - tau|, where tau = (1+sqrt(5))/2 (golden ratio).

0, 2, 6, 15, 26, 40, 58, 79, 104, 131, 162, 196, 233, 273, 317, 364, 414, 468, 524, 584, 647, 714, 783, 856, 932, 1011, 1094, 1180, 1269, 1361, 1456, 1555, 1657, 1762, 1870, 1982, 2097, 2215, 2336, 2461, 2589

Offset

0,2

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

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

a(n) = A293400(n) if (fractional part of tau*n^2) < 1/2, else a(n) = A293401(n).

Mathematica

z = 120; r = GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A293400 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293401 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293402 *)

Crossrefs

Cf. A001622, A293400, A293401.

Sequence in context: A153274 A091766 A269706 * A192691 A360405 A256313

Adjacent sequences: A293399 A293400 A293401 * A293403 A293404 A293405

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2017

Status

approved