Non-ideal PTE solutions for degrees above 11

[Saša Mb]

Hello everyone.

I am currently looking for information on the smallest known cardinalities of non-ideal solutions to the Prouhet–Tarry–Escott problem for degrees above 11 (valid for r=1 to k).

Someone recently suggested that the OEIS archives may contain sequences related to known PTE solution sizes. I searched the OEIS but was unable to find...

Could you please tell me whether such information is available in OEIS? Or where? I need explicit solutions, both sets.

Any pointers would be greatly appreciated.

Thanks.

Best regards,

Saša

[Ruud H.G. van Tol]

On 2026-06-01 12:54, Saša Mb wrote:
> I am currently looking for information on the smallest known
cardinalities of non-ideal solutions to the Prouhet–Tarry–Escott problem
for degrees above 11 (valid for r=1 to k).
> Someone recently suggested that the OEIS archives may contain
sequences related to known PTE solution sizes. I searched the OEIS but
was unable to find...

Not sure what you meant by "archives".

For non-ideal, see for example the recent A395962, though that came up
with a simple search, so you likely already saw that.

> [...]

-- Ruud

[M F Hasler]

On Mon, Jun 1, 2026 at 6:54 AM Saša Mb <sasam...@gmail.com> wrote:

I am currently looking for information on the smallest known cardinalities of non-ideal solutions to the Prouhet–Tarry–Escott problem for degrees above 11 (valid for r=1 to k).

If you do a search for the 3 names:

https://oeis.org/search?q=Prouhet+Tarry+Escott&go=Search

there are 19 hits. Maybe you find something useful there.

-M.