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A217843
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Numbers which are the sums of consecutive nonnegative cubes.
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15
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0, 1, 8, 9, 27, 35, 36, 64, 91, 99, 100, 125, 189, 216, 224, 225, 341, 343, 405, 432, 440, 441, 512, 559, 684, 729, 748, 775, 783, 784, 855, 1000, 1071, 1196, 1241, 1260, 1287, 1295, 1296, 1331, 1584, 1728, 1729, 1800, 1925, 1989, 2016, 2024, 2025, 2197
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history;
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OFFSET
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1,3
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COMMENTS
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Contains A000578 (cubes), A005898 (two consecutive cubes), A027602 (three consecutive cubes), A027603 (four consecutive cubes) etc. - R. J. Mathar, Nov 04 2012
See A265845 for sums of consecutive positive cubes in more than one way. - Reinhard Zumkeller, Dec 17 2015
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) >> n^2. Probably a(n) ~ kn^2 for some k but I cannot prove this. - Charles R Greathouse IV, Aug 07 2013
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MATHEMATICA
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nMax = 3000; t = {0}; Do[k = n; s = 0; While[s = s + k^3; s <= nMax, AppendTo[t, s]; k++], {n, nMax^(1/3)}]; t = Union[t]
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PROG
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(Haskell)
import Data.Set (singleton, deleteFindMin, insert, Set)
a217843 n = a217843_list !! (n-1)
a217843_list = f (singleton (0, (0, 0))) (-1) where
f s z = if y /= z then y : f s'' y else f s'' y
where s'' = (insert (y', (i, j')) $
insert (y' - i ^ 3 , (i + 1, j')) s')
y' = y + j' ^ 3; j' = j + 1
((y, (i, j)), s') = deleteFindMin s
-- Reinhard Zumkeller, Dec 17 2015, May 12 2015
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CROSSREFS
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Cf. A034705, A217844-A217850, A062682, A131643, A240137.
Cf. A000578, A005898, A027602, A027603.
Cf. A265845 (subsequence).
Sequence in context: A042311 A003997 A114090 * A139753 A046874 A225364
Adjacent sequences: A217840 A217841 A217842 * A217844 A217845 A217846
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, Oct 23 2012
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STATUS
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approved
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