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A201053 Nearest cube.

%I A201053 #26 Aug 15 2022 04:33:25
%S A201053 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,
%T A201053 27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,64,64,64,64,64,64,
%U A201053 64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64
%N A201053 Nearest cube.
%C A201053 a(n) = if n-A048763(n) < A048762(n)-n then A048762(n) else A048763(n);
%C A201053 apart from 0, k^3 occurs 3*n^2+1 times, cf. A056107.
%H A201053 Reinhard Zumkeller, <a href="/A201053/b201053.txt">Table of n, a(n) for n = 0..10000</a>
%F A201053 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
%F A201053 Sum_{n>=1} 1/a(n)^2 = Pi^4/30 + Pi^6/945. - _Amiram Eldar_, Aug 15 2022
%p A201053 seq(k^3 $ (3*k^2+1), k=0..10); # _Robert Israel_, Jan 03 2017
%t A201053 Module[{nn=70,c},c=Range[0,Ceiling[Surd[nn,3]]]^3;Flatten[Array[ Nearest[ c,#]&,nn,0]]] (* _Harvey P. Dale_, May 27 2014 *)
%o A201053 (Haskell)
%o A201053 a201053 n = a201053_list !! n
%o A201053 a201053_list = 0 : concatMap (\x -> replicate (a056107 x) (x ^ 3)) [1..]
%o A201053 (Python)
%o A201053 from sympy import integer_nthroot
%o A201053 def A201053(n):
%o A201053     a = integer_nthroot(n,3)[0]
%o A201053     return a**3 if 2*n < a**3+(a+1)**3 else (a+1)**3 # _Chai Wah Wu_, Mar 31 2021
%Y A201053 Cf. A061023, A074989, A053187 (nearest square), A000578.
%Y A201053 Cf. A048762, A048763, A056107.
%K A201053 nonn,look
%O A201053 0,6
%A A201053 _Reinhard Zumkeller_, Nov 28 2011