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
Keywords
Examples
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
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
Programs
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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 -
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 *) -
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
Extensions
Missing a(23)-a(24) from Charles R Greathouse IV, Nov 16 2012