A181138 Least positive integer k such that n^2 + k is a cube.

1, 7, 4, 18, 11, 2, 28, 15, 61, 44, 25, 4, 72, 47, 20, 118, 87, 54, 19, 151, 112, 71, 28, 200, 153, 104, 53, 271, 216, 159, 100, 39, 307, 242, 175, 106, 35, 359, 284, 207, 128, 47, 433, 348, 261, 172, 81, 535, 440, 343, 244, 143, 40, 566, 459, 350, 239, 126, 11

Offset: 0

Author

Jason Earls, Oct 06 2010

Keywords

• nonn
• easy

Comments

a(n) = A070923(n) if n is not cube. Zak Seidov, Mar 26 2013

See A229618 for the range of this sequence. A179386 gives the range of b(n) = min{ a(m); m >= n }. The indices of jumps in this sequence are given in A179388 = { n | a(m)>a(n) for all m > n } = { 0, 5, 11, 181, 207, 225, 500, 524, 1586, ... }. - M. F. Hasler, Sep 26 2013

Examples

			a(11) = 4 because 11^2 + k is never a cube for k < 4, but 11^2 + 4 = 5^3. - _Bruno Berselli_, Jan 29 2013
		

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000 (Corrected Jan 19 2019)

Crossrefs

Cf. A070923, A077116.

Programs

Magma

S:=[];
k:=1;
for n in [0..60] do
   while not IsPower(n^2+k,3) do
        k:=k+1;
   end while;
   Append(~S, k);
   k:=1;
end for;
S;  // Bruno Berselli, Jan 29 2013

Mathematica

Table[(1 + Floor[n^(2/3)])^3 - n^2, {n, 100}] (* Zak Seidov, Mar 26 2013 *)

PARI

A181138(n)=(sqrtnint(n^2,3)+1)^3-n^2 \\ Charles R Greathouse IV, Mar 26 2013

Formula

a(n) << n^(4/3). - Charles R Greathouse IV, Mar 26 2013

Extensions

Extended to a(0)=1 by M. F. Hasler, Sep 26 2013