# [seqfan] Re: conjectured largest number which is not the sum of an n-almost prime and a prime.

Jonathan Post jvospost3 at gmail.com
Mon Mar 30 02:34:56 CEST 2009

```I accept all of Franklin T. Adams-Watters corrections and warnings. I
did not submit the seq yet because it does need to be checked more
deeply by someone with a better platform than I have.

There's certainly a lot of dithering even at the start of underlying
seqs, such as:

Number of distinct ways to express n as the sum of a semiprime and a prime:

n  a(n)
1   0
2   0
3   0
4   0
5   0
6   1
7   1
8   1
9   2
10   0
11  3
12  2
13  2
14  1
15  3
16  2
17  5
18  1
19  2
20  2
21  3
22  2
23  4
24  2
25  3
26  3
27  5
28  5
29  4
30  1
31  2
32  4
33  5
34  2
35  4
36  3
37  5
...

On Sun, Mar 29, 2009 at 5:23 PM,  <franktaw at netscape.net> wrote:
> If this is submitted, the title should be "Largest number which is not
> the sum of an n-almost prime and a prime", not "Conjectured largest
> ....".  That all the values are conjectured belongs in a comment.
>
> I would be reluctant to conjecture the value of a(6) below without
> checking past 10^9 -- probably at least to 10^10.  Large gaps near the
> end of these sequences seem to be the rule rather than the exception.
>
>
>
> -----Original Message-----
> From: Jonathan Post <jvospost3 at gmail.com>
>
> Connecting these seqs:
> A130588      Integers which are not the sum of a 3-almost prime and a
> prime.
> A146295      Integers which are not the sum of a 4-almost prime and a
> prime.
> A146296      Integers which are not the sum of a 5-almost prime and a
> prime.
> A146297      Integers which are not the sum of a 6-almost prime and a
> prime.
>
> we get the following... ALL of whose values are conjectures, although
> checked through 10^9
>
> a(n) is the conjectured largest number which is not the sum of an
> n-almost prime and a prime.
> n=2,3,4,5,6: a(n) = 10, 300, 60060, 3573570, 446185740
>
> These are not as artificial as they seem, as they derive from Chen's
> approach to proving Goldbach's conjecture.
>
>
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```