# [seqfan] Re: Smallest k yielding primes of form a(n) = a(n-1) + n*k

Neil Sloane njasloane at gmail.com
Fri Nov 7 00:28:17 CET 2014

```of course they are worth submitting!  in general, the answer to that
question is almost always yes

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.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

On Thu, Nov 6, 2014 at 1:06 PM, Bob Selcoe <rselcoe at entouchonline.net>
wrote:

> Hello Seqfans,
>
> Let sequence K(p) start with a(1) being an odd prime (p).  Let a(n) =
> a(n-1) + n*k, where k is the smallest number such that a(n) is prime.
>
> This yields two sequences, K(p) and S(p), where S(p) is the sequence of
> primes generated by K(p).  All K(p) and S(p) are unique.
>
> Results for p = {3,5,7}, are:
>
>       n 1 2 3 4 5 6 7 8 9 10
>
>       K(3) 3 1 2 2 2 2 6 3 8 2
>       S(3) 3 5 11 19 29 41 83 107 179 199
>
>       K(5) 5 1 2 1 4 1 4 1 2 1
>       S(5) 5 7 13 17 37 43 71 79 97 107
>
>       K(7) 7 2 2 3 6 2 6 3 4 2
>       S(7) 7 11 17 29 59 71 113 137 173 193
>
>
>
> S(3) is (essentially) A084697.  Otherwise, I can't find any other related
> OEIS sequences - even when starting with a(2).
>
> Might the first few be worth submitting?
>
> Cheers,
> Bob Selcoe
>
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>

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