A062682 Numbers that are sums of two or more consecutive (positive) cubes in more than 1 way.

33075, 89559, 105525, 164800, 188784, 189189, 353241, 443456, 608391, 1271600, 2370816, 3132116, 3132675, 3184236, 5821200, 9018000, 9769375, 11437525, 20793591, 22153600, 24359616, 28685440, 47651373, 55454525, 56078784, 61765200, 77053284

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Example

33075 = 11^3 + 12^3 + ... + 19^3 = 15^3 + 16^3 + ... + 20^3.
The first number having three representations is 246153726441216 = (2144^3 + ... + 5631^3) = (3047^3 + ... + 5720^3) = (8072^3 + ... + 8504^3). - Robert G. Wilson v, Nov 16 2012

Mathematica

nn = 10^10; t1 = {}; s = 1; i = 1; While[i++; s = s + i^3; s < nn/2, AppendTo[t1, s]]; t = t1; i = 0; While[Length[t1] > 1, i++;  t1 = Rest[t1] - i^3; t = Join[t, t1]]; t = Select[t, # < t1[[1]] &]; t2 = Sort[Select[Tally[t], #[[2]] > 1 &]]; Transpose[t2][[1]] (* T. D. Noe, Nov 16 2012 *)

Prog

(PARI) list(lim)=my(v=List(), u=v, s, y); for(x=1, (lim\2)^(1/3), s=x^3; y=x; while(1, s+=y++^3; if(s>lim, break, listput(v, s)))); v=vecsort(Vec(v)); for(i=2, #v, if(v[i]==v[i-1], listput(u, v[i]))); vecsort(Vec(u), , 8) \\ Charles R Greathouse IV, Nov 16 2012
(Haskell)
import Data.Set (singleton, deleteFindMin, insert, Set)
a062682 n = a062682_list !! (n-1)
a062682_list = f (singleton (1 + 2^3, (1, 2))) 0 0 where
   f s z z' = if y == z && z' /= z then y : f s'' y z else f s'' y z
              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 16 2015

Crossrefs

Subsequence of A265377 and of A265845.

Sequence in context: A237624 A118278 A118280 * A094889 A332200 A031660

Adjacent sequences: A062679 A062680 A062681 * A062683 A062684 A062685

Keyword

nonn

Author

Erich Friedman, Jul 04 2001

Extensions

Missing a(23)-a(24) from Charles R Greathouse IV, Nov 16 2012

Status

approved