A002821 a(n) = nearest integer to n^(3/2). (Formerly M2437 N0964)

0, 1, 3, 5, 8, 11, 15, 19, 23, 27, 32, 36, 42, 47, 52, 58, 64, 70, 76, 83, 89, 96, 103, 110, 118, 125, 133, 140, 148, 156, 164, 173, 181, 190, 198, 207, 216, 225, 234, 244, 253, 263, 272, 282, 292, 302, 312, 322, 333, 343, 354, 364, 375, 386, 397

Offset

0,3

References

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

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.

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

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

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

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Formula

a(n) = floor(n^(3/2) + 1/2). - Ridouane Oudra, Nov 13 2019

a(n) = sqrt(A077118(n)). - Chai Wah Wu, Jul 30 2022

Maple

A002821 := proc(n)
    round(n^(3/2)) ;
end proc:
seq(A002821(n), n=0..100) ;

Mathematica

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 *)

Prog

(Haskell)
a002821 = round . sqrt . fromIntegral . (^ 3)
-- Reinhard Zumkeller, Jul 11 2014
(Python)
from math import isqrt
def A002821(n): return (m:=isqrt(k:=n**3))+int((k-m*(m+1)<<2)>=1) # Chai Wah Wu, Jul 30 2022

Crossrefs

Cf. A000093, A077118.

Sequence in context: A081401 A003311 A108279 * A046992 A001463 A145197

Adjacent sequences: A002818 A002819 A002820 * A002822 A002823 A002824

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved