cp's OEIS Frontend

A268510 Numbers x such that x^2 = y^3 + z (0 < abs(z) < y).

%I A268510 #20 Mar 21 2016 21:23:13
%S A268510 3,5,11,47,58,70,181,207,225,253,282,312,375,419,500,524,985,1015,
%T A268510 1138,1586,1710,1746,1874,1986,2315,2619,2723,2765,3788,4072,4120,
%U A268510 5511,5644,5805,5859,6022,6159,6576,6717,7002,7320,7970,8030,8669,10615,10681,13252,13537,13788,13860,14113,14404,16725,17537,17615
%N A268510 Numbers x such that x^2 = y^3 + z (0 < abs(z) < y).
%C A268510 List of n such as n^2 is a near cube (see examples).
%C A268510 Numbers x such that x^2 = y^3 + 0 (e.g. 1000^2 = 100^3) are omitted.
%C A268510 Note that a delta of 17 appears often. See A029728.
%H A268510 Daniel Mondot, <a href="/A268510/b268510.txt">Table of n, a(n) for n = 1..10000</a>
%e A268510 3^2 = 2^3 + 1
%e A268510 5^2 = 3^3 - 2
%e A268510 11^2 = 5^3 - 4
%e A268510 47^2 = 13^3 + 12
%e A268510 58^2 = 15^3 - 11
%e A268510 70^2 = 17^3 - 13
%e A268510 181^2 = 32^3 - 7
%e A268510 207^2 = 35^3 - 26
%e A268510 225^2 = 37^3 - 28
%e A268510 253^2 = 40^3 + 9
%e A268510 282^2 = 43^3 + 17
%e A268510 312^2 = 46^3 + 8
%e A268510 375^2 = 52^3 + 17
%e A268510 419^2 = 56^3 - 55
%e A268510 500^2 = 63^3 - 47
%e A268510 524^2 = 65^3 - 49
%e A268510 985^2 = 99^3 - 74
%t A268510 Select[Range@ 5000, Resolve@ Exists[{y, z}, And[Reduce[#^2 == (y^3 + z), {y, z}, Integers], 0 < Abs@ z < y]] &] (* _Michael De Vlieger_, Feb 07 2016 *)
%Y A268510 Cf. A029728, A268509, A253181.
%K A268510 nonn
%O A268510 1,1
%A A268510 _Daniel Mondot_, Feb 06 2016