A268510 - OEIS

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

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OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A029728, A268509, A253181.

Sequence in context: A049883 A059242 A175173 * A004203 A201473 A088884

Adjacent sequences: A268507 A268508 A268509 * A268511 A268512 A268513

KEYWORD

nonn

AUTHOR

Daniel Mondot, Feb 06 2016

STATUS

approved