A061023 Difference between the closest square and the closest cube to n.

0, 0, 0, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 11, 11, 11, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 22, 22, 22, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 17, 17, 17, 17, 17

Offset: 0

Author

Hareendra Yalamanchili (hyalaman(AT)mit.edu), May 24 2001

Keywords

• easy
• nice
• nonn
• look

Comments

a(A201217(n)) = 0.

Examples

			a(46)=15 because the nearest square is 49 and the nearest cube is 64 and 64 - 49 = 15.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000290, A000578.

Programs

Haskell

a061023 n = abs (a053187 n - a201053 n)
a061023_list = map a061023 [0..]
-- Reinhard Zumkeller, Nov 28 2011

Mathematica

dsc[n_]:=Module[{s=Floor[Sqrt[n]],c=Floor[Power[n, (3)^-1]],ns,nc}, ns= Nearest[{s^2,(s+1)^2},n]; nc=Nearest[{c^3,(c+1)^3},n];Abs[nc-ns]]; Flatten[ Array[dsc,100,0]] (* Harvey P. Dale, Aug 19 2011 *)

PARI

{ for (n=0, 10000, x=n^(1/2); s=floor(x)^2; t=ceil(x)^2; if (n-s > t-n, s=t); x=n^(1/3); c=floor(x)^3; d=ceil(x)^3; if (n-c > d-n, c=d); write("b061023.txt", n, " ", abs(c-s)) ) } \\ Harry J. Smith, Jul 16 2009

Formula

a(n) = abs(A053187(n) - A201053(n)). [Reinhard Zumkeller, Nov 28 2011]

Extensions

More terms from Harvey P. Dale, Aug 19 2011