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A265377 Sums of two or more consecutive positive cubes. 3
9, 35, 36, 91, 99, 100, 189, 216, 224, 225, 341, 405, 432, 440, 441, 559, 684, 748, 775, 783, 784, 855, 1071, 1196, 1241, 1260, 1287, 1295, 1296, 1584, 1729, 1800, 1925, 1989, 2016, 2024, 2025, 2241, 2331, 2584, 2800, 2925, 2989, 3016, 3024, 3025, 3059, 3060 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All numbers of the form A000537(b) - A000537(a) for 0 <= a <= b-2.
A217843 minus (A000578 minus A131643).
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.
If a(k(n)) = A000537(n+1), k(n) >= A000217(n) for n > 0. - Altug Alkan, Dec 07 2015
See A062682 for sums of two or more consecutive positive cubes in more than one way. - Reinhard Zumkeller, Dec 16 2015
LINKS
EXAMPLE
a(1) = 1^3 + 2^3 = 9.
a(2) = 2^3 + 3^3 = 35.
a(3) = 1^3 + 2^3 + 3^3 = 36.
MAPLE
amin:= proc(b, N) local r;
r:= b^2*(b+1)^2 - 4*N; if r > 0 then iroot(r, 4) else 1 fi
end proc:
A265377:= proc(N) # to get all terms <= N
local a, b;
sort(convert(select(`<=`, {seq(seq(b^2*(b+1)^2/4 - a^2*(a-1)^2/4,
a = amin(b, N) .. b-1), b=2..1+iroot(floor(N/2), 3))}, N), list))
end proc:
A265377(10000);
MATHEMATICA
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 *)
PROG
(Haskell)
import Data.Set (singleton, deleteFindMin, insert, Set)
a265377 n = a265377_list !! (n-1)
a265377_list = f (singleton (1 + 2^3, (1, 2))) (-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
CROSSREFS
Subset of A217843.
Cf. A062682 (subsequence).
Sequence in context: A067960 A119757 A003865 * A187554 A338010 A267702
KEYWORD
nonn
AUTHOR
Robert Israel, Dec 07 2015
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)