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

Maximilian Hasler maximilian.hasler at gmail.com
Wed Jan 7 17:59:34 CET 2009

```I agree that the sequence

A153971 Numbers p susch that 2^(p-1)+3 is not prime.

merits  "uned", "obsc".

I observed that all listed numbers are = 11 (mod 12)
which is not the case for all primes s.th.2^(p-1)+3 is prime.

But this is not sufficient.to explain the missing terms (then starting with 47).
(Adding "primes =11 (mod 12)" one would get
11,23,47,59,71,83,107,131,167,179,191,227,239,251,263,311,347,359,383,...)

Also, the comment is strange.
The "conjecture" does not merit that name (since already 37 is a
counter-example).

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

On Wed, Jan 7, 2009 at 10:43 AM, Edwin Clark <eclark at math.usf.edu> wrote:
> The sequence A153971 is incorrectly defined:
(...)
> Note that if p = 6 then 2^(p-1)+3 = 35, but 6 is not in the
> listed numbers. Next guess: definition should be only primes p such that
> 2^(p-1)+3 is not prime, but then 37 should be in the list, yet it is not.

```