A293407 -id:A293407 - cp's OEIS frontend

A293408 The integer k that minimizes |k/n^2 - 1/tau|, where tau = (1+sqrt(5))/2 (golden ratio).

0, 1, 2, 6, 10, 15, 22, 30, 40, 50, 62, 75, 89, 104, 121, 139, 158, 179, 200, 223, 247, 273, 299, 327, 356, 386, 418, 451, 485, 520, 556, 594, 633, 673, 714, 757, 801, 846, 892, 940, 989, 1039, 1090, 1143, 1197, 1252, 1308, 1365, 1424, 1484, 1545, 1608, 1671

Offset: 0

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Clark Kimberling, Oct 11 2017

nonn
easy

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

Cf. A001622, A293402, A293404, A152738, A293407.

z = 120; r = -11+GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A152738 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293407 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293408 *)

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

a(n) = A152738(n) if (fractional part of (1/tau)*n^2) < 1/2, else a(n) = A293407(n).

cp's OEIS Frontend

A293408 The integer k that minimizes |k/n^2 - 1/tau|, where tau = (1+sqrt(5))/2 (golden ratio).

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