A266528 Least positive integer x such that n + x^5 = y^2 + z^3 for some positive integers y and z, or 0 if no such x exists.

8, 1, 8, 3, 1, 2, 11, 5, 1, 1, 42, 1, 2, 11, 3, 21, 1, 3, 2, 5, 2, 3, 3, 1, 7, 1, 3, 1, 22, 4, 1, 2, 1, 2, 8, 1, 1, 3, 5, 13, 2, 2, 1, 1, 2, 27, 3, 3, 2, 1, 2, 1, 7, 6, 3, 5, 1, 2, 7, 2, 5, 15, 1, 17, 1, 13, 4, 1, 2, 2, 86

Offset

0,1

Comments

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

Links

Zhi-Wei Sun, Table of n, a(n) for n = 0..1100

Example

a(0) = 8 since 0 + 8^5 = 104^2 + 28^3.
a(2) = 8 since 2 + 8^5 = 179^2 + 9^3.
a(6) = 11 since 6 + 11^5 = 143^2 + 52^3.
a(10) = 42 since 10 + 42^5 = 11415^2 + 73^3.
a(15) = 21 since 15 + 21^5 = 1355^2 + 131^3.
a(435) = 3019 since 435 + 3019^5 = 475594653^2 + 290845^3.

Mathematica

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

Crossrefs

Cf. A000290, A000578, A000584, A266152, A266153, A266212, A266215, A266230, A266231, A266277, A266314, A266363, A266364.

Sequence in context: A010689 A070637 A070651 * A010519 A238214 A019760

Adjacent sequences: A266525 A266526 A266527 * A266529 A266530 A266531

Keyword

nonn

Author

Zhi-Wei Sun, Dec 31 2015

Status

approved