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

%I A062682 #24 Dec 17 2015 00:07:59
%S A062682 33075,89559,105525,164800,188784,189189,353241,443456,608391,1271600,
%T A062682 2370816,3132116,3132675,3184236,5821200,9018000,9769375,11437525,
%U A062682 20793591,22153600,24359616,28685440,47651373,55454525,56078784,61765200,77053284
%N A062682 Numbers that are sums of two or more consecutive (positive) cubes in more than 1 way.
%H A062682 Charles R Greathouse IV, <a href="/A062682/b062682.txt">Table of n, a(n) for n = 1..1000</a>
%e A062682 33075 = 11^3 + 12^3 + ... + 19^3 = 15^3 + 16^3 + ... + 20^3.
%e A062682 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
%t A062682 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 *)
%o A062682 (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
%o A062682 (Haskell)
%o A062682 import Data.Set (singleton, deleteFindMin, insert, Set)
%o A062682 a062682 n = a062682_list !! (n-1)
%o A062682 a062682_list = f (singleton (1 + 2^3, (1, 2))) 0 0 where
%o A062682    f s z z' = if y == z && z' /= z then y : f s'' y z else f s'' y z
%o A062682               where s'' = (insert (y', (i, j')) $
%o A062682                            insert (y' - i ^ 3 , (i + 1, j')) s')
%o A062682                     y' = y + j' ^ 3; j' = j + 1
%o A062682                     ((y, (i, j)), s') = deleteFindMin s
%o A062682 -- _Reinhard Zumkeller_, Dec 16 2015
%Y A062682  Subsequence of A265377 and of A265845.
%K A062682 nonn
%O A062682 1,1
%A A062682 _Erich Friedman_, Jul 04 2001
%E A062682 Missing a(23)-a(24) from _Charles R Greathouse IV_, Nov 16 2012