A303268 Least y for which x^6 + y^7 = A300568(n)^8 for some x > 1.

573308928, 664301250000, 699840000000

Offset

1,1

Comments

The values listed here are the y-values corresponding to the z-values listed in A300568. The x-values are then readily computed as (z^8 - y^7)^(1/6).

See the main entry A300567 for all further information.

Links

Table of n, a(n) for n=1..3.

Example

A300568(1) = 47775744 is the smallest z such that z^8 = x^6 + y^7 for some x, y > 1, and the smallest such y is a(1) = 12*z = 573308928. It then follows that x = (47775744^8 - 573308928^7)^(1/6) = 13759414272 = 288*z.
A300568(2) = 22143375000 is the second smallest z such that z^8 = x^6 + y^7 for some x, y > 1, and the smallest corresponding y is a(2) = 30*z = 664301250000. It then follows that x = (22143375000^8 - 664301250000^7)^(1/6) = 29893556250000 = 1350*z.
Similarly, a(3) = 30*A300568(2) = 699840000000 is the smallest y for which x = (A300568(3)^8 - y^7)^(1/6) is an integer, here x = 1800*A300568(3) = 60*a(3).

Crossrefs

Cf. A300564, A300565, A300566, A300567, A300568, A303265, A303266, A303267.

Sequence in context: A234199 A071135 A335561 * A186961 A032755 A234391

Adjacent sequences: A303265 A303266 A303267 * A303269 A303270 A303271

Keyword

nonn

Author

M. F. Hasler, May 04 2018

Status

approved