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

0,4

Comments

a(A201217(n)) = 0.

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000290, A000578.

Sequence in context: A351348 A246011 A329310 * A355954 A057690 A318706

Adjacent sequences: A061020 A061021 A061022 * A061024 A061025 A061026

Keyword

easy,nice,nonn,look

Author

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

Extensions

More terms from Harvey P. Dale, Aug 19 2011

Status

approved