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A201053 Nearest cube. 10
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A195139 A010731 A048762 * A160949 A245401 A048763
KEYWORD
nonn,look
AUTHOR
Reinhard Zumkeller, Nov 28 2011
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)