A129965 Triangular numbers that are the difference of nonnegative cubes.
0, 1, 91, 4095, 5886, 7875, 8128, 8911, 9045, 17955, 21736, 23653, 47278, 93961, 115921, 130816, 184528, 259560, 379756, 488566, 575128, 658378, 758296, 810901, 873181, 885115, 1060696, 1155960, 1358776, 1385280, 1997001, 2616328, 2685403
Offset: 1
Keywords
Examples
A000217(13) = Sum_{k=1..13} k = 91 = 216 - 125 = 6^3 - 5^3, so 91 is in the sequence. - _Peter Munn_, Dec 05 2022
Links
- Robert Israel, Table of n, a(n) for n = 1..439 (terms <= 10^12)
Programs
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Maple
M:= 10^7: # for terms <= M S:= {0}: for x from 1 while 3*x^2 - 3*x + 1 < M do if x^3 < M then Y:= 0 else Y:= ceil(x^3-M) fi; S:= S union select(t -> issqr(1+8*t),{seq(x^3 - y^3, y = Y .. x-1)}); od: sort(convert(S,list)); # Robert Israel, Dec 05 2023 -
Mathematica
With[{n = 5000}, Intersection[(#1*((#1 + 1)/2) & ) /@ Range[0, n], Flatten[Outer[ #1^3 - #2^3 &, Range[n], Range[0, n - 1]]]]]