A293404 - OEIS

A293404

Least integer k such that k/n^2 > (3 + sqrt(5))/2 (the golden ratio).

0, 3, 11, 24, 42, 66, 95, 129, 168, 213, 262, 317, 377, 443, 514, 590, 671, 757, 849, 946, 1048, 1155, 1268, 1385, 1508, 1637, 1770, 1909, 2053, 2202, 2357, 2516, 2681, 2852, 3027, 3208, 3393, 3585, 3781, 3983, 4189, 4401, 4619, 4841, 5069, 5302, 5540, 5784

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OFFSET

0,2

LINKS

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

FORMULA

a(n) = ceiling(r*n^2), where r = (3 + sqrt(5))/2.

a(n) = A293403(n) + 1 for n > 0.

MATHEMATICA

z = 120; r = 1+GoldenRatio;

Table[Floor[r*n^2], {n, 0, z}]; (* A293403 *)

Table[Ceiling[r*n^2], {n, 0, z}]; (* A293404 *)