A300763 a(n) = ceiling(n/g^3), where g = (1+sqrt(5))/2 is the golden ratio.

0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18

Offset: 0

Author

Jeffrey Shallit, Jul 02 2018

Keywords

• nonn

Links

• Altug Alkan, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001622, A019446, which is ceiling(n/g), A189663, which is ceiling(n/g^2) (but shifted by one).

Cf. A098317.

Programs

Mathematica

Array[Ceiling[#/GoldenRatio^3] &, 90, 0] (* Robert G. Wilson v, Jul 02 2018 *)

PARI

a(n) = my(t=2+sqrt(5)); ceil(n/t); \\ Altug Alkan, Jul 02 2018

Formula

a(n) = ceiling(n/t) where t = 2*g + 1 = 2 + sqrt(5). - Altug Alkan, Jul 02 2018