A077110 Nearest integer cube to n^2.

0, 1, 1, 8, 8, 27, 27, 64, 64, 64, 125, 125, 125, 125, 216, 216, 216, 343, 343, 343, 343, 512, 512, 512, 512, 729, 729, 729, 729, 729, 1000, 1000, 1000, 1000, 1000, 1331, 1331, 1331, 1331, 1331, 1728, 1728, 1728, 1728, 1728, 2197, 2197, 2197

Offset

0,4

Links

Table of n, a(n) for n=0..47.

Formula

a(n) = if A075847(n) < A070923(n) then A077106(n) else A077107(n).

Example

a(10)=125, as 125=5^3 is the nearest cube to 100=10^2.

Mathematica

nic[n_]:=Module[{n2=n^2, s3, c1, c2}, s3=Surd[n2, 3]; c1=Floor[s3]^3; c2= Ceiling[ s3]^3; If[n2-c1<c2-n2, c1, c2]]; Array[nic, 50, 0] (* Harvey P. Dale, Jul 05 2015 *)

Prog

(Python)
from sympy import integer_nthroot
def A077110(n):
    n2 = n**2
    a = integer_nthroot(n2, 3)[0]
    a2, a3 = a**3, (a+1)**3
    return a3 if a3+a2-2*n2 < 0 else a2 # Chai Wah Wu, Sep 24 2021

Crossrefs

Cf. A000578, A000290, A077111, A077118.

Cf. A002760 (Squares and cubes). - Zak Seidov, Oct 08 2015

Sequence in context: A318542 A319089 A003873 * A333625 A098360 A133038

Adjacent sequences: A077107 A077108 A077109 * A077111 A077112 A077113

Keyword

nonn

Author

Reinhard Zumkeller, Oct 29 2002

Status

approved