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

0,2

Links

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

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).

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 *)

Crossrefs

Cf. A001622, A293402, A293403, A293404.

Sequence in context: A231116 A272953 A259443 * A029880 A144413 A033811

Adjacent sequences: A293402 A293403 A293404 * A293406 A293407 A293408

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2017

Status

approved