

A181138


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


8



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
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OFFSET

0,2


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


LINKS

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


FORMULA

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


EXAMPLE

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


MATHEMATICA

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


PROG

(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
(PARI) a(n)=(sqrtnint(n^2, 3)+1)^3n^2 \\ Charles R Greathouse IV, Mar 26 2013
(PARI) A181138(n)=(n^(2/3)\(1.1^precision(1.))+1)^3n^2 \\ In the current stable version 2.5.5, the function sqrtnint is not yet introduced, it exists only in development versions from PARI V.2.6 on. Unfortunately, in the standard precision, floor(125^(2/3))=24.  M. F. Hasler, Sep 26 2013


CROSSREFS

Cf. A070923, A077116.
Sequence in context: A297938 A298549 A279806 * A279942 A279998 A063632
Adjacent sequences: A181135 A181136 A181137 * A181139 A181140 A181141


KEYWORD

nonn,easy


AUTHOR

Jason Earls, Oct 06 2010


EXTENSIONS

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


STATUS

approved



