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) A181138(n)=(sqrtnint(n^2, 3)+1)^3-n^2 \\ Charles R Greathouse IV, Mar 26 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jason Earls, Oct 06 2010
EXTENSIONS
Extended to a(0)=1 by M. F. Hasler, Sep 26 2013
STATUS
approved