A113768 a(1) = 1, a(n+1) = a(n) + floor(a(n)^(1/3)).

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 224, 230, 236, 242, 248, 254, 260

Offset: 1

Author

Jonathan Vos Post, Jan 19 2006

Keywords

• nonn
• easy

Comments

First 17 terms identical to A079645 (Integer part of the cube root of n divides n). Replacing cube root by square root gives A033638.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033638, A048766, A079645.

Programs

Magma

[n le 1 select 1 else Self(n-1)+Floor(Self(n-1)^(1/3)): n in [1..75]]; // Vincenzo Librandi, Jul 29 2019

Maple

A[1]:= 1:
for n from 1 to 100 do A[n+1] := A[n] + floor(A[n]^(1/3)) od:
seq(A[i],i=1..100); # Robert Israel, Jul 28 2019

Mathematica

NestList[#+Floor[Surd[#,+3]]&,1,70] (* Harvey P. Dale, Jan 21 2013 *)

Formula

Conjecture: a(n) ~ (2/3)*n*sqrt((2/3)*n). - José María Grau Ribas, Feb 13 2024

Extensions

Corrected and extended by Harvey P. Dale, Jan 21 2013