[seqfan] Re: A property of 163

Max Alekseyev maxale at gmail.com
Fri Jul 10 16:31:01 CEST 2009

On Fri, Jul 10, 2009 at 9:50 AM, Tanya
Khovanova<mathoflove-seqfan at yahoo.com> wrote:
> Dear SeqFans,
> I received the following submission for my number gossip page (numbergossip.com) from Anand Deopurkar:
> "A unique property of 163: It is the largest number n such that the integers in the imaginary quadratic extension Q(\sqrt -n) have the unique factorization property."
> Can some confirm this?

That's true.
See http://en.wikipedia.org/wiki/Class_number_(number_theory)#Class_numbers_of_quadratic_fields

> He also sent a sequence which is not in the database:
> "Integers in the following imaginary quadratic fields Q(\sqrt -n) have the unique factorization property: n = 1,2,4,7,11,19,43,67,163. So you could add this as a rare property for those integers as well."
> Should we add the sequence?

4 should not be in this sequence. And it's already in the OEIS - A003173


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