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

0, 3, 10, 24, 42, 65, 94, 128, 168, 212, 262, 317, 377, 442, 513, 589, 670, 757, 848, 945, 1047, 1155, 1267, 1385, 1508, 1636, 1770, 1909, 2053, 2202, 2356, 2516, 2681, 2851, 3026, 3207, 3393, 3584, 3780, 3982, 4189, 4401, 4618, 4841, 5069, 5302, 5540, 5783

Offset: 0

Author

Clark Kimberling, Oct 11 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A001622, A293402, A293403, A293404.

Programs

Mathematica

z = 120; r = 1+GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A293403 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293404 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293405 *)

Formula

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

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