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A293408 The integer k that minimizes |k/n^2 - 1/tau|, where tau = (1+sqrt(5))/2 (golden ratio). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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).

MATHEMATICA

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 *)

CROSSREFS

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

Sequence in context: A133931 A050895 A184426 * A097022 A137236 A124198

Adjacent sequences:  A293405 A293406 A293407 * A293409 A293410 A293411

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 11 2017

STATUS

approved

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Last modified June 4 10:43 EDT 2020. Contains 334825 sequences. (Running on oeis4.)