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A293400
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Greatest integer k such that k/n^2 < (1 + sqrt(5))/2 (the golden ratio).
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3
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0, 1, 6, 14, 25, 40, 58, 79, 103, 131, 161, 195, 232, 273, 317, 364, 414, 467, 524, 584, 647, 713, 783, 855, 931, 1011, 1093, 1179, 1268, 1360, 1456, 1554, 1656, 1762, 1870, 1982, 2096, 2215, 2336, 2461, 2588
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = floor(r*n^2), where r = (1 + sqrt(5))/2.
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MATHEMATICA
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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 *)
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PROG
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(Magma) [Floor((1 + Sqrt(5))/2*n^2) : n in [0..80]]; // Wesley Ivan Hurt, Jul 03 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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