A293400 -id:A293400 - cp's OEIS frontend

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

Clark Kimberling, Oct 11 2017

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

Cf. A001622, A293400, A293401.

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 *)

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).

A293401 Least integer k such that k/n^2 > (1 + sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

0, 2, 7, 15, 26, 41, 59, 80, 104, 132, 162, 196, 233, 274, 318, 365, 415, 468, 525, 585, 648, 714, 784, 856, 932, 1012, 1094, 1180, 1269, 1361, 1457, 1555, 1657, 1763, 1871, 1983, 2097, 2216, 2337, 2462, 2589

Offset: 0

Clark Kimberling, Oct 11 2017

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

Cf. A001622, A293400, A293402.

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 *)

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

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

cp's OEIS Frontend

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

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