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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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

Crossrefs

Cf. A000093, A077118.

Programs

Haskell

a002821 = round . sqrt . fromIntegral . (^ 3)
-- Reinhard Zumkeller, Jul 11 2014

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-fltHarvey P. Dale, May 12 2011 *)

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

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