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A002821
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a(n) = nearest integer to n^(3/2).
(Formerly M2437 N0964)
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6
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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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).
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LINKS
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FORMULA
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MAPLE
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[ seq(round(eval(n^(3/2))), n=0..100) ];
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a002821 = round . sqrt . fromIntegral . (^ 3)
(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
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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