# [seqfan] Re: What in the next one? [primes isolated from squarefrees]

Neil Sloane njasloane at gmail.com
Tue Jan 26 01:27:21 CET 2016

```Chris, what was the definition of this one? 2, 17, 727, 47527, 29002021
(note typo above), 494501773?

Are you looking at the squarefree nonprimes S, and  asking
for the smallest prime p such that the nearest element of S differs from p
by at least n (starting at n=1)?
No, that doesn't work. I'm having trouble seeing how you got 2 and then 17
rather than 5 or 7.

Could you please submit it to the OEIS, and also the other one you mention (1,
17, 26, 2526, 5876126, 8061827, ...)?

Thanks!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Wed, Jan 20, 2016 at 1:10 PM, Chris Thompson <cet1 at cam.ac.uk> wrote:

> On Dec 25 2015, юрий герасимов wrote:
>
> Prime numbers, isolated from neighboring squarefrees by > n:  2, 17, 727,
>> 47527, 2902021, ...
>>
>> What in the next one?
>>
>
> No-one seems to have followed up on this, for some reason...
>
> The series starts 2, 17, 727, 47527, 29002021 (note typo above), 494501773
>
> But although "successively more isolated primes" appear in OEIS as
> http://oeis.org/A023186 we don't yet have "successively more isolated
> square-free numbers" (without the prime requirement), which should start
> 1, 17, 26, 2526, 5876126, 8061827, ... (the next term is >10^9) doesn't.
>
> It seems to me that might be of more interest, possibly even leading to
> heroic computations along the lines of http://arxiv.org/abs/1210.3829
> as mentioned in http://oeis.org/A045882
>
> --
> Chris Thompson
> Email: cet1 at cam.ac.uk
>
>
>
>
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```