A002821 - OEIS

%I M2437 N0964 #33 Sep 02 2024 08:36:43

%S 0,1,3,5,8,11,15,19,23,27,32,36,42,47,52,58,64,70,76,83,89,96,103,110,

%T 118,125,133,140,148,156,164,173,181,190,198,207,216,225,234,244,253,

%U 263,272,282,292,302,312,322,333,343,354,364,375,386,397

%N a(n) = nearest integer to n^(3/2).

%D M. Boll, Tables Numériques Universelles. Dunod, Paris, 1947, p. 46.

%D M. Hall, Jr., The Diophantine equation x^3-y^2=k, pp. 173-198 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

%D A. V. Lebedev and R. M. Fedorova, A Guide to Mathematical Tables. Pergamon, Oxford, 1960, p. 17.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002821/b002821.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor(n^(3/2) + 1/2). - _Ridouane Oudra_, Nov 13 2019

%F a(n) = sqrt(A077118(n)). - _Chai Wah Wu_, Jul 30 2022

%p A002821 := proc(n)

%p     round(n^(3/2)) ;

%p end proc:

%p seq(A002821(n),n=0..100) ;

%t t[n_]:=Module[{flt=Floor[n],cet=Ceiling[n]},If[n-flt<cet-n,flt, cet]]; t/@(Range[0,60]^((3/2))) (* _Harvey P. Dale_, May 12 2011 *)

%o (Haskell)

%o a002821 = round . sqrt . fromIntegral . (^ 3)

%o -- _Reinhard Zumkeller_, Jul 11 2014

%o (Python)

%o from math import isqrt

%o def A002821(n): return (m:=isqrt(k:=n**3))+int((k-m*(m+1)<<2)>=1) # _Chai Wah Wu_, Jul 30 2022

%Y Cf. A000093, A077118.

%K nonn,easy,nice

%O 0,3

%A _N. J. A. Sloane_