A266231 Least positive integer x such that x^2 - n = y^3 + z^3 for some positive integers y and z, or 0 if no such x exists.

6, 2, 61, 47, 3283, 16, 3, 6, 5, 8, 12, 686, 16, 4, 302, 5, 13, 12, 152, 6, 7, 83, 5, 148, 33, 37, 6, 10, 8, 11, 34, 16, 7, 6, 10, 8, 24, 53, 16, 7, 13, 52, 13, 14, 30, 9, 7, 8, 11, 67, 74, 22, 9, 28, 8, 11, 43, 115, 20, 122, 23, 8, 14, 48, 9, 25, 11, 14, 392, 14

Offset

1,1

Comments

The conjecture in A266230 implies that a(n) > 0 for all n > 0.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

 a(1) = 6 since 6^2 - 1 = 2^3 + 3^3.
a(3) = 61 since 61^2 - 3 = 7^3 + 15^3.
a(4) = 47 since 47^2 - 4 = 2^3 + 13^3.
a(5) = 3283 since 3283^2 - 5 = 65^3 + 219^3.
a(166) = 6554 since 6554^2 - 166 = 175^3 + 335^3.
a(635) = 44779 since 44779^2 - 635 = 25^3 + 1261^3.

Mathematica

CQ[n_]:=CQ[n]=IntegerQ[n^(1/3)]
Do[x=Floor[Sqrt[n]]+1; Label[bb]; Do[If[CQ[-n+x^2-y^3], Print[n, " ", x]; Goto[aa]], {y, 1, ((-n+x^2)/2)^(1/3)}]; x=x+1; Goto[bb]; Label[aa]; Continue, {n, 1, 70}]

Crossrefs

Cf. A000290, A000578, A003325, A266152, A266153, A266212, A266230.

Sequence in context: A373829 A242529 A263088 * A192355 A100251 A266607

Adjacent sequences: A266228 A266229 A266230 * A266232 A266233 A266234

Keyword

nonn

Author

Zhi-Wei Sun, Dec 24 2015

Status

approved