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A293402 The integer k that minimizes |k/n^2 - tau|, where tau = (1+sqrt(5))/2 (golden ratio). 6
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 (list; graph; refs; listen; history; text; internal format)
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 A256313 A138621

Adjacent sequences:  A293399 A293400 A293401 * A293403 A293404 A293405

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 11 2017

STATUS

approved

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Last modified June 5 01:27 EDT 2020. Contains 334828 sequences. (Running on oeis4.)