A154840 Distance to nearest cube different from n.

1, 1, 1, 2, 3, 3, 2, 1, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 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, 37, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

Offset

0,4

Comments

Equals A074989(n) if this is not zero, else 1+A055400(n-1), the distance to the nearest cube < n.

Links

Table of n, a(n) for n=0..80.

Example

a(8)=7, because the two cubes below and above 8 are 1^3=1 and 3^3=27, and the distance to 1 is smaller, namely 8-1=7.

Maple

distNearstDiffCub := proc(n) local iscbr ; iroot(n, 3, 'iscbr') ; if iscbr then 1+A055400(n-1); else A074989(n) ; end if; end proc;

Mathematica

dnc[n_]:=Module[{c=Surd[n, 3]}, If[IntegerQ[c], n-(c-1)^3, Min[n-Floor[ c]^3, Ceiling[c]^3-n]]]; Array[dnc, 90, 0] (* Harvey P. Dale, Mar 30 2019 *)

Crossrefs

Cf. A066635, A163497.

Sequence in context: A156613 A285555 A078041 * A309995 A205102 A348760

Adjacent sequences: A154837 A154838 A154839 * A154841 A154842 A154843

Keyword

nonn,easy

Author

R. J. Mathar, Nov 01 2009

Status

approved