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 2020-08-02, 01:28 #45 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 23×3×79 Posts Won't be anytime soon. I am only hoping it will be in my lifetime. I have to retool my setup for the next iteration. I intend to try a better sieving method so it will be some time before it's ready. But thanks for the compliment. Last fiddled with by a1call on 2020-08-02 at 01:29
2020-08-02, 05:48   #46
Citrix

Jun 2003

112×13 Posts

Quote:
 Originally Posted by a1call There is currently no established way of showing the integer in a reduced form, but it would be quite easy to invent one.
I am not sure if you are aware or not - your sequence is a recursive quadratic polynomial. You can just specify the seed and the depth level.

x_next=f(x) where f(x)=x^2-x+1

2-->3-->7-->43-->

For sieve:-
Factors would be of format factor==1 (mod 6)
Also given the recurrent nature you can easily calculate which depth level a prime p will divide.

Last fiddled with by Citrix on 2020-08-02 at 05:55 Reason: typo

2020-08-03, 00:31   #47
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

111011010002 Posts

Quote:
 Originally Posted by Citrix I am not sure if you are aware or not - your sequence is a recursive quadratic polynomial. You can just specify the seed and the depth level. x_next=f(x) where f(x)=x^2-x+1 2-->3-->7-->43--> For sieve:- Factors would be of format factor==1 (mod 6) Also given the recurrent nature you can easily calculate which depth level a prime p will divide.
This is a very old thread and the concept has evolved since the OP.
Your definition seems to relate to N-1 flavour with k=1.
The oeis sequence is the N+1 flavour. There are two primary iteration-flavours and infinite combinations of the 2 are possible. The k-always-equal-1 is problematic since any (large) non-prime iteration will render the later iterations non-provable. The modular logic you point out is very helpful and should speed things up. Thank you very much.
I am lost in your last sentence, but I assume regardless that, the necessary depth will be beyond what can be executed for a 400k dd integer so perhaps we can leave it at that.
Again thanks for the insight.

Last fiddled with by a1call on 2020-08-03 at 00:55