# [seqfan] Re: A relation between A153971 and A098828?

David Wilson dwilson at gambitcomm.com
Wed Jan 7 18:54:11 CET 2009

```Maximilian Hasler wrote:
> Inspired by the second part of the comment, I think I found the inteded meaning:
>
>  for(n=1,99, isprime(  p = 2*n^2 + 6*n + 3 ) & !isprime(2^(p-1)+3) &
> print1(p","))
> 11,23,59,83,179,263,311,419,479,683,839,1103,1511,2111,2243,2663,2963,3119,4139,4703,5099,5303,5939,7079,10223,11399,12011,12323,12959,17483,19403,
>
> So it should be
>
> A153971 Primes of the form p = 2*n^2 + 6*n + 3  such that 2^(p-1)+3 is
> not prime.
>
> But personnally I find this a quite arbitrary definition....
>
> Maximilian
>
>
All primes (indeed all numbers) of the form p = 2n^2 + 6n + 3 have
2^(p-1)+3 divisible by 7 or 13. Thus the only p for which 2^(p-1)+3 is
prime is p = 3 with 2^(p-1)+3 = 7. All prime p > 3 yield 2^(p-1)+3 > 13,
and being divisible by 7 or 13, is composite. So your sequence becomes

A153971 Primes of the form p = 2n^2 + 6n + 3 except p = 3.

which is to say, A098828 with 3 omitted. Not worth keeping.

Even if we tweak A153971 to "Primes p with 2^(p-1)+3 composite" and add
in missing values, it is still a pretty contorted definition. Better
would be the more inclusive "Numbers with 2^p+3 prime", that is, A057732.

Maybe a mercy killing is in order.

```