# [seqfan] Re: 2^prime(n) - prime(n^2)

Neil Sloane njasloane at gmail.com
Sat Oct 12 17:05:30 CEST 2013

```Interesting!

n*Prime[Prime[n]] - Prime[n] = 1, 7, 28, 61, 144, 233, 396, 517, 724, 1061,
…

Here are a few more terms:

1, 7, 28, 61, 144, 233, 396, 517, 724, 1061, 1366, 1847, 2286, 2631, 3118,
3803,
4650, 5033, 6222, 6989, 7634, 8743, 9830, 10975, 12628, 14121, 15098,
16329,
17262, 18397, 21852, 23517, 25372, 26959, 29916, 31421, 33846, 36583,
38482,
41067, 43404, 45473, 49388, 51331, 53848, 55783, 60748, 67409, 69990,
72121

For a slower rate of growth, one can consider

a(n) = n*prime(prime(n)) - prime(n)^2.

which I just submitted as A230098.

Neil

On Sat, Oct 12, 2013 at 4:47 AM, Veikko Pohjola <veikko at nordem.fi> wrote:

> Playing with primes has no end. After a couple of minutes of playing with
> Mathematica I got the following which is not in OEIS either:
> n*Prime[Prime[n]] - Prime[n] = 1, 7, 28, 61, 144, 233, 396, 517, 724,
> 1061, …
>
> I'm wondering is it solely up to my personal judgement whether this one
> (or any similarly discovered) might have such a general interest that it
>  deserves the submission to OEIS, or is there some "moral duty" that, once
> discovered, also this kind of findings, kind of, ought to be? If the latter
> is not true, I would not submit.
>
> Veikko
>
>
> Neil Sloane kirjoitti 11.10.2013 kello 4.25:
>
> > Only three terms, but plenty of digits in them - so please enter
> > it into the OEIS, someone!
> > Neil
> >
> >
> > On Thu, Oct 10, 2013 at 7:47 PM, Charles Greathouse <
> > charles.greathouse at case.edu> wrote:
> >
> >> I agree with Harvey's terms. If there are any others they have more than
> >> 3000 decimal digits.
> >>
> >> Charles Greathouse
> >> Analyst/Programmer
> >> Case Western Reserve University
> >>
> >>
> >> On Thu, Oct 10, 2013 at 5:30 PM, Harvey P. Dale <hpd at hpdale.org> wrote:
> >>
> >>>        I get different terms: 2, 1951, 147573952589676410491.
> >>>        Best,
> >>>        Harvey
> >>>
> >>>
> >>> -----Original Message-----
> >>> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of ????
> >>> ?????????
> >>> Sent: Thursday, October 10, 2013 1:01 PM
> >>> To: seqfan at list.seqfan.eu
> >>> Subject: [seqfan] 2^prime(n) - prime(n^2)
> >>>
> >>>
> >>> Hello, SeqFans,
> >>>
> >>> Primes of form 2^prime(n) - prime(n^2):
> >>>
> >>> 2, 129193,... What in the next one?
> >>>
> >>> Best regards,
> >>>
> >>> JSG
> >>>
> >>> _______________________________________________
> >>>
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> >>>
> >>> _______________________________________________
> >>>
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
> >
> > --
> > Dear Friends, I have now retired from AT&T. New coordinates:
> >
> > 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
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
> _______________________________________________
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>

--
Dear Friends, I have now retired from AT&T. New coordinates:

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.