[seqfan] Re: A327265 and A309981

[hv at crypt.org]

"M. F. Hasler" <oeis at hasler.fr> wrote:
:Do we have a formal proof that any n has a tau signature?

>From any n, if you take the signature far enough to show two odd numbers
then it is guaranteed to be enough to identify n: they have to represent
two consecutive squares (of whatever prime signature).

So if I have it right, A309981(n) <= (ceil(sqrt(n)) + 1)^2 - n.

Using your definitions I would also write |t(n)| = A309981(n) + 1
(which to me feels like a more natural quantity to consider than
A309981(n) itself).

Hugo