A181138 - OEIS

%I #36 Aug 11 2024 05:23:47

%S 1,7,4,18,11,2,28,15,61,44,25,4,72,47,20,118,87,54,19,151,112,71,28,

%T 200,153,104,53,271,216,159,100,39,307,242,175,106,35,359,284,207,128,

%U 47,433,348,261,172,81,535,440,343,244,143,40,566,459,350,239,126,11

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

%C a(n) = A070923(n) if n is not cube. _Zak Seidov_, Mar 26 2013

%C 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

%H Bruno Berselli, <a href="/A181138/b181138.txt">Table of n, a(n) for n = 0..1000</a> (Corrected Jan 19 2019)

%F a(n) << n^(4/3). - _Charles R Greathouse IV_, Mar 26 2013

%e 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

%t Table[(1 + Floor[n^(2/3)])^3 - n^2, {n, 100}] (* _Zak Seidov_, Mar 26 2013 *)

%o (Magma)

%o S:=[];

%o k:=1;

%o for n in [0..60] do

%o    while not IsPower(n^2+k,3) do

%o         k:=k+1;

%o    end while;

%o    Append(~S, k);

%o    k:=1;

%o end for;

%o S;  // _Bruno Berselli_, Jan 29 2013

%o (PARI) A181138(n)=(sqrtnint(n^2,3)+1)^3-n^2 \\ _Charles R Greathouse IV_, Mar 26 2013

%Y Cf. A070923, A077116.

%K nonn,easy

%O 0,2

%A _Jason Earls_, Oct 06 2010

%E Extended to a(0)=1 by _M. F. Hasler_, Sep 26 2013