# [seqfan] Re: New sequence

M. F. Hasler seqfan at hasler.fr
Mon Apr 10 22:39:53 CEST 2017

```On Mon, Apr 10, 2017 at 4:27 AM, Vladimir Shevelev <shevelev at bgu.ac.il>
wrote:

> can be upgraded to "If there is
> another it is > 500001"
>

looking at http://oeis.org/A046927/graph suggests
that the number of decompositions 2n+1 = p +2q
grows strongly enough that it is increasingly improbable
that all of the resulting possibilities be composite.

PS1: the following PARI code checks this up to n=2*10^5 in about 2 seconds
and up to 5e5 in 8 seconds:

is(n)=!forprime(q=2,n\2-1,isprime(n-2*q)&&(isprime(n+2*
q)||isprime(3*n-4*q))&&return)
forstep(n=1,5e5,2,is(n)&&print1(n","))
1,3,5,59,151.

PS2: it would be interesting to add a comment which explains the "bands"
seen in http://oeis.org/A046927/graph.

-Maximilian

I wanted to consider the sequence of odd n
> for which n+2p and n+2q are both composites
> for all pairs (p,q) such that p+2q=n.
> For example, 9 is not in the sequence,
> since 9+2*2=13, although 5+2*2=9.
> By handy I found that the first member
> is 59 (here the pairs (13,23), (37,11), (53,3))
> and all n+2p, n+2q are composites.
> Comparing to A284919, I was very surprised
> that up to 2*10^4 Peter Moses has found only
> more one term 151.
>

```