A074989 Distance from n to nearest cube.

0, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Offset: 0

Author

Zak Seidov, Oct 02 2002

Keywords

• nonn

Comments

a(n)=0 when n is a cube; between zeros local maxima are of form 3/2 k(k-1).

Examples

			a(3) = 2 because the nearest cube to 3 is 1 and distance from 3 to 1 is 2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to distance to nearest element of some set

Crossrefs

Cf. A053188 (distance from n to nearest square).

Cf. A201053, A000578.

Programs

Haskell

a074989 0 = 0
a074989 n = min (n - last xs) (head ys - n) where
   (xs,ys) = span (< n) a000578_list
-- Reinhard Zumkeller, Nov 28 2011

Maple

A074989 := proc(n) local iscbr ; iroot(n,3,'iscbr') ; if iscbr then 0; else iscbr := floor(n^(1/3)) ; min((iscbr+1)^3-n, n-iscbr^3) ; end if; end proc; # R. J. Mathar, Nov 01 2009

Mathematica

dnc[n_]:=Module[{cr=Surd[n,3]},Min[n-Floor[cr]^3,Ceiling[cr]^3-n]]; Array[ dnc,90,0] (* Harvey P. Dale, Jan 24 2015 *)

Python

from sympy import integer_nthroot
def A074989(n):
    a = integer_nthroot(n,3)[0]
    return min(n-a**3,(a+1)**3-n) # Chai Wah Wu, Mar 31 2021

Extensions

a(0) added and offset changed by Reinhard Zumkeller, Nov 28 2011