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A293405 The integer k that minimizes |k/n^2 - tau^2|, where tau = (1+sqrt(5))/2 (golden ratio). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A231116 A272953 A259443 * A029880 A144413 A033811
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 11 2017
STATUS
approved

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Last modified June 12 23:46 EDT 2024. Contains 373362 sequences. (Running on oeis4.)