# [seqfan] Re: Sieving method for composite numbers described / used in A146071

Maximilian Hasler maximilian.hasler at gmail.com
Fri Oct 31 20:49:55 CET 2008

```PS:
I think the following primes will never appear:

13,61,73,109,151,181,229,241,257,293,307,313,349,353,373,397,409,487,509,557,571,577,601,613,643,653,661,709,727,733,739,751,761,773,811,823,937,941,977,...

I obtained them (certainly not in a n optimized way) using the idea
from my previous mail:

primes_notin_A145834()={
local(n=1,t=0,k);forprime(p=1,999,while(n<2*(p+2),isprime(k=A145834x(n++))
| next; t=bitor(1<<primepi(k),t));bittest(t,primepi(p)) |
print1(p","))}

with

A145834x(n)=n-sum(i=1,#n=factor(n)~,n[1,i]*n[2,i])

(which is not exactly equal to A145834 but extends that function
defined on composites to the domain of all numbers.)

A145834(n)=for(k=0,primepi(n),isprime(n++)&k--);n+0-sum(i=1,#n=factor(n)~,n[1,i]*n[2,i])

Maximilian

On Fri, Oct 31, 2008 at 15:14, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
> I think you have A145834(n) > n/2 - 2 or something alike,
> so any prime that does not appear in due time in this sequence will
> never appear in it and thus will not appear in A146071.
>
> I don't know either if a method *using* the complete prime
> factorization of the numbers can be considered as a "sieving" method
> for prime numbers.
> It's a bit like "if n>1 is not prime, subtract 1 and start over, else
> stop" (which of course yields all primes).
>
> Maximilian
>
> On Fri, Oct 31, 2008 at 13:00, Alexander Povolotsky <apovolot at gmail.com> wrote:
>> Hi,
>>
>> Would the sieving method for composite numbers, with which I came up in
>> A146071,
>> produce ALL prime  numbers (so far I don't see 13 there ... ;-) ) ?
>> If NOT - then could one define / predict what prime numbers will be not
>> generated by below described sieving method for composite numbers ?
>>
>>
>> Thanks,
>> Best Regards,
>> Alexander R. Povolotsky
>>
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>>
>

```