[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.
>
> Franklin T. Adams-Watters
>
>
> -----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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