[seqfan] Re: A generalization of "antipodes": primes and highly composite numbers

Olivier Gerard olivier.gerard at gmail.com
Fri Jul 22 13:06:43 CEST 2016


On Fri, Jul 22, 2016 at 10:37 AM, Vladimir Shevelev <shevelev at bgu.ac.il>
wrote:

> Dear SeqFans,
>
> I with Peter submitted 12 sequences:
> A275246, 248,249,251,252,253 and
> A275239, 240,241,242,243,244 .
>
> The first series is devoted to the following
> generalization of primes:
>
> [...]

>
> The second series in the similar manner
> is devoted to a generalization of highly
> composite numbers (A002182).
>

[...]

>
> Note that the sequence of highly composite
> numbers of kind h>=1 begins from Prime(h+1)
> (which is a unique prime in this sequence).
>
> Did anyone hear about such or closed type of
> generalizations?
>
>
No I haven't heard of something exactly like this
but this is typically the kind of generalization
that might interest number theorists, people
working on additive number theory and
master conjecturers such as Zhi Wei Sun
for instance.

You and Peter Moses could probably ask about this on mathoverflow and on
the NumberTheory list  (
https://listserv.nodak.edu/cgi-bin/wa.exe?A0=NMBRTHRY)
if you want but do not do that until your sequences have been approved in a
first public version: draft edits are not available or searchable for the
general public.

Regards,

Olivier


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