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A217843 Numbers which are the sums of consecutive nonnegative cubes. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

a(n) >> n^2. Probably a(n) ~ kn^2 for some k but I cannot prove this. - Charles R Greathouse IV, Aug 07 2013

MATHEMATICA

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]

PROG

(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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

T. D. Noe, Oct 23 2012

STATUS

approved

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Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.