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

3, 5, 11, 47, 58, 70, 181, 207, 225, 253, 282, 312, 375, 419, 500, 524, 985, 1015, 1138, 1586, 1710, 1746, 1874, 1986, 2315, 2619, 2723, 2765, 3788, 4072, 4120, 5511, 5644, 5805, 5859, 6022, 6159, 6576, 6717, 7002, 7320, 7970, 8030, 8669, 10615, 10681, 13252, 13537, 13788, 13860, 14113, 14404, 16725, 17537, 17615

Offset: 1

Author

Daniel Mondot, Feb 06 2016

Keywords

• nonn

Comments

List of n such as n^2 is a near cube (see examples).

Numbers x such that x^2 = y^3 + 0 (e.g. 1000^2 = 100^3) are omitted.

Note that a delta of 17 appears often. See A029728.

Examples

			3^2 = 2^3 + 1
5^2 = 3^3 - 2
11^2 = 5^3 - 4
47^2 = 13^3 + 12
58^2 = 15^3 - 11
70^2 = 17^3 - 13
181^2 = 32^3 - 7
207^2 = 35^3 - 26
225^2 = 37^3 - 28
253^2 = 40^3 + 9
282^2 = 43^3 + 17
312^2 = 46^3 + 8
375^2 = 52^3 + 17
419^2 = 56^3 - 55
500^2 = 63^3 - 47
524^2 = 65^3 - 49
985^2 = 99^3 - 74
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A029728, A268509, A253181.

Programs

Mathematica

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 *)