A266985 Least positive integer x such that n + x^3 = y^2 + z^5 for some positive integers y and z, or 0 if no such x exists.

7, 1, 2, 34, 1, 55, 3, 5, 30, 1, 3, 242, 6, 7, 3, 26, 1, 4, 2, 7, 5, 3, 62, 3, 77, 1, 107, 10, 2, 2, 3, 6, 1, 2, 128, 1, 1, 4, 3, 11, 1, 3, 2, 6, 7, 5, 22, 1, 50, 1, 7, 5, 6, 16, 3, 3, 1, 2, 4, 62, 2, 17, 19, 6, 1, 8, 14, 1, 4, 3, 11

Offset

0,1

Comments

The general conjecture in A266277 implies that for any integer m there are positive integers x, y and z with m + x^3 = y^2 + z^5.

See also A266277 and A266528 for similar conjectures.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 0..3800

Example

a(0) = 7 since 0 + 7^3 = 10^2 + 3^5.
a(3) = 34 since 3 + 34^3 = 150^2 + 7^5.
a(8) = 30 since 8 + 30^3 = 101^2 + 7^5.
a(11) = 242 since 11 + 242^3 = 3420^2 + 19^5.
a(766) = 90891 since 766 + 90891^3 = 11850281^2 + 906^5.

Mathematica

SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]
Do[x=1; Label[bb]; Do[If[SQ[n+x^3-y^5], Print[n, " ", x]; Goto[aa]], {y, 1, (n+x^3-1)^(1/5)}]; x=x+1; Goto[bb]; Label[aa]; Continue, {n, 0, 70}]

Crossrefs

Cf. A000290, A000578, A000584, A266152, A266153, A266230, A266231, A266314, A266363, A266364, A266528, A266548.

Sequence in context: A316953 A317733 A258335 * A286912 A239807 A130875

Adjacent sequences: A266982 A266983 A266984 * A266986 A266987 A266988

Keyword

nonn

Author

Zhi-Wei Sun, Jan 08 2016

Status

approved