A359275 a(n) = greatest integer k such that (n+k)^2 <= n^3.

0, 0, 0, 2, 4, 6, 8, 11, 14, 18, 21, 25, 29, 33, 38, 43, 48, 53, 58, 63, 69, 75, 81, 87, 93, 100, 106, 113, 120, 127, 134, 141, 149, 156, 164, 172, 180, 188, 196, 204, 212, 221, 230, 238, 247, 256, 265, 275, 284, 294, 303, 313, 322, 332, 342, 352, 363, 373

Offset

0,4

Links

Table of n, a(n) for n=0..57.

Formula

a(n) = -n + [n^(3/2)], where [ ] = floor.

Example

a(7) = 11 because (7+11)^2 <= 7^3 < (7+12)^2.

Mathematica

a[n_] := Select[-1 + Range[1300], (n + #)^2 <= n^3 < (n + # + 1)^2 &]
Flatten[Table[a[n], {n, 0, 100}]]

Crossrefs

Cf. A000290, A000578.

Sequence in context: A339573 A060655 A117490 * A032514 A011858 A183144

Adjacent sequences: A359272 A359273 A359274 * A359276 A359277 A359278

Keyword

nonn

Author

Clark Kimberling, Jan 26 2023

Status

approved