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A265377 Sums of two or more consecutive positive cubes.

%I A265377 #29 Dec 25 2015 15:01:00
%S A265377 9,35,36,91,99,100,189,216,224,225,341,405,432,440,441,559,684,748,
%T A265377 775,783,784,855,1071,1196,1241,1260,1287,1295,1296,1584,1729,1800,
%U A265377 1925,1989,2016,2024,2025,2241,2331,2584,2800,2925,2989,3016,3024,3025,3059,3060
%N A265377 Sums of two or more consecutive positive cubes.
%C A265377 All numbers of the form A000537(b) - A000537(a) for 0 <= a <= b-2.
%C A265377 A217843 minus (A000578 minus A131643).
%C A265377 n is in the sequence iff n = s*t where (s+t)/2 = A000217(u) and (s-t)/2 = A000217(v) with u-v >= 2.
%C A265377 If a(k(n)) = A000537(n+1), k(n) >= A000217(n) for n > 0. - _Altug Alkan_, Dec 07 2015
%C A265377 See A062682 for sums of two or more consecutive positive cubes in more than one way. - _Reinhard Zumkeller_, Dec 16 2015
%H A265377 Robert Israel, <a href="/A265377/b265377.txt">Table of n, a(n) for n = 1..10000</a>
%e A265377 a(1) = 1^3 + 2^3 = 9.
%e A265377 a(2) = 2^3 + 3^3 = 35.
%e A265377 a(3) = 1^3 + 2^3 + 3^3 = 36.
%p A265377 amin:= proc(b,N) local r;
%p A265377   r:= b^2*(b+1)^2 - 4*N; if r > 0 then iroot(r,4) else 1 fi
%p A265377 end proc:
%p A265377 A265377:= proc(N) # to get all terms <= N
%p A265377   local  a,b;
%p A265377   sort(convert(select(`<=`,{seq(seq(b^2*(b+1)^2/4 - a^2*(a-1)^2/4,
%p A265377        a = amin(b,N) .. b-1), b=2..1+iroot(floor(N/2),3))},N),list))
%p A265377 end proc:
%p A265377 A265377(10000);
%t A265377 With[{nn=12},Select[Sort[Flatten[Table[Total/@Partition[Range[nn]^3,n,1],{n,2,nn}]]],#<=((nn(nn+1))/2)^3&]] (* _Harvey P. Dale_, Dec 25 2015 *)
%o A265377 (Haskell)
%o A265377 import Data.Set (singleton, deleteFindMin, insert, Set)
%o A265377 a265377 n = a265377_list !! (n-1)
%o A265377 a265377_list = f (singleton (1 + 2^3, (1, 2))) (-1) where
%o A265377    f s z = if y /= z then y : f s'' y else f s'' y
%o A265377               where s'' = (insert (y', (i, j')) $
%o A265377                            insert (y' - i ^ 3 , (i + 1, j')) s')
%o A265377                     y' = y + j' ^ 3; j' = j + 1
%o A265377                     ((y, (i, j)), s') = deleteFindMin s
%o A265377 -- _Reinhard Zumkeller_, Dec 17 2015
%Y A265377 Subset of A217843.
%Y A265377 Cf. A000217, A000537, A000578, A131643.
%Y A265377 Cf. A062682 (subsequence).
%K A265377 nonn
%O A265377 1,1
%A A265377 _Robert Israel_, Dec 07 2015