A201053 Nearest cube.

0, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64

Offset

0,6

Comments

a(n) = if n-A048763(n) < A048762(n)-n then A048762(n) else A048763(n);

apart from 0, k^3 occurs 3*n^2+1 times, cf. A056107.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

G.f.: (1-x)^(-1)*Sum_{k>=0} (3*k^2+3*k+1)*x^((k+1)*(k^2+k/2+1)). - Robert Israel, Jan 03 2017

Sum_{n>=1} 1/a(n)^2 = Pi^4/30 + Pi^6/945. - Amiram Eldar, Aug 15 2022

Maple

seq(k^3 $ (3*k^2+1), k=0..10); # Robert Israel, Jan 03 2017

Mathematica

Module[{nn=70, c}, c=Range[0, Ceiling[Surd[nn, 3]]]^3; Flatten[Array[ Nearest[ c, #]&, nn, 0]]] (* Harvey P. Dale, May 27 2014 *)

Prog

(Haskell)
a201053 n = a201053_list !! n
a201053_list = 0 : concatMap (\x -> replicate (a056107 x) (x ^ 3)) [1..]
(Python)
from sympy import integer_nthroot
def A201053(n):
    a = integer_nthroot(n, 3)[0]
    return a**3 if 2*n < a**3+(a+1)**3 else (a+1)**3 # Chai Wah Wu, Mar 31 2021

Crossrefs

Cf. A061023, A074989, A053187 (nearest square), A000578.

Cf. A048762, A048763, A056107.

Sequence in context: A195139 A010731 A048762 * A160949 A245401 A048763

Adjacent sequences: A201050 A201051 A201052 * A201054 A201055 A201056

Keyword

nonn,look

Author

Reinhard Zumkeller, Nov 28 2011

Status

approved