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A293400 Greatest integer k such that k/n^2 < (1 + sqrt(5))/2 (the golden ratio). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Felipe Gonçalves, Diogo Oliveira e Silva, João P. G. Ramos, New Sign Uncertainty Principles, arXiv:2003.10771 [math.CA], 2020.

FORMULA

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

a(n) = A293401(n) - 1 for n > 0.

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 *)

PROG

(MAGMA) [Floor((1 + Sqrt(5))/2*n^2) : n in [0..80]]; // Wesley Ivan Hurt, Jul 03 2020

CROSSREFS

Cf. A001622, A293401, A293402.

Sequence in context: A185594 A095794 A119867 * A026055 A288939 A165986

Adjacent sequences:  A293397 A293398 A293399 * A293401 A293402 A293403

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 11 2017

STATUS

approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)