A113769 a(1) = 1, a(n+1) = a(n) + round(a(n)^(1/3)).

1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 176, 182, 188, 194, 200, 206, 212, 218, 224, 230, 236, 242, 248, 254

Offset: 1

Author

Jonathan Vos Post, Jan 19 2006

Keywords

• easy
• nonn

Comments

A033638 a(0) = 1; a(1) = 1; for n > 1 a(n) = a(n-1) + round(sqrt(a(n-1))). Hence the current sequence is analogous to A033638, but with cube root instead of square root.

Examples

			a(19) = 43, so a(20) = a(19) + round(a(19)^(1/3)) = 43 + round(43^(1/3)) = 43 + round(3.50339806) = 43 + 4 = 47.
a(31) = 91, so a(32) = a(31) + round(a(31)^(1/3)) = 91 + round(4.49794145) = 91 + 4 = 95.
a(32) = 95, so a(33) = a(32) + round(a(32)^(1/3)) = 95 + round(4.56290264) = 95 + 5 = 100.
a(47) = 170, so a(48) = 170 + round(170^(1/3)) = 170 + round(5.53965826) = 176.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A033638, A113768 (flooring instead rounding).

Programs

Mathematica

NestList[#+Round[Surd[#,3]]&,1,60] (* Harvey P. Dale, Jan 12 2019 *)

Formula

a(1) = 1, a(n+1) = a(n) + round(a(n)^(1/3)).