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-   -   PARI's commands (https://www.mersenneforum.org/showthread.php?t=13636)

3.14159 2010-09-01 14:04

[QUOTE=science_man_88]it's up, and doesn't look like he did.
[/QUOTE]

Meh, I made the corrections myself. All Charles needs to do is add the b-file. Or, if I think of a working script, I can do this myself!

science_man_88 2010-09-01 14:12

[QUOTE=3.14159;228026]Meh, I made the corrections myself. All Charles needs to do is add the b-file. Or, if I think of a working script, I can do this myself![/QUOTE]

pretty sure I got it working if i declare it in 2 parts

[CODE](11:08) gp > w(x) = x^x
%85 = (x)->x^x
(11:09) gp > w(4)
%86 = 256
(11:10) gp > w(4)
%87 = 256
(11:10) gp > kbb(a, x, m) = { if(x<w(m), for(n=a, x, if(isprime(n*m^m+1), print1(n*m^m+1, ", ")) )); }
(11:10) gp > kbb(1,3,4)
257, 769,[/CODE]

science_man_88 2010-09-01 14:18

[CODE]kbb(a, x, m) = if(x<m^m, for(n=a, x, if(isprime(n*m^m+1), print1(n*m^m+1, ", ")) ))[/CODE]

this one works on my end to give the same result in one function.

science_man_88 2010-09-01 14:25

if you want them in order pass them to to a vector then use vecsort() to sort them oh and if you want to loop until a specific n you could add loops then call this script to print for all x<m^m etc.

3.14159 2010-09-01 14:30

[QUOTE=science_man_88]if you want them in order pass them to to a vector then use vecsort() to sort them oh and if you want to loop until a specific n you could add loops then call this script to print for all x<m^m etc.
[/QUOTE]

Yes, yes, I'm working on the sequence's b-file. Unless Charles decided to hinder my efforts by sending it first.

science_man_88 2010-09-01 14:31

[QUOTE=3.14159;228031]Yes, yes, I'm working on the sequence's b-file.[/QUOTE]

I was just giving suggestions as I know what's likely to be asked.

3.14159 2010-09-01 14:39

[QUOTE=science_man_88]I was just giving suggestions as I know what's likely to be asked.
[/QUOTE]

I give up. I'll let Charles work on that. I'll work on the sequence, with no restriction. In this case, b > 1. (This means the set of 4n + 1 primes is a subset of this sequence.)

CRGreathouse 2010-09-01 14:51

Here's what I submitted:
[code]%I A180362
%S A180362 5,13,109,163,257,271,379,433,487,541,769,3329,7681,7937,9473,10753,11777,
%T A180362 12289,13313,14081,14593,15361,17921,18433,19457,22273,23041,23297,25601,
%U A180362 26113,26881,30977,31489,32257,36097,36353,37501,37633,37889,39937,40193
%N A180362 Primes of the form k * n^n + 1 with k < n^n.
%C A180362 A result of Heath-Brown shows, on the GRH, that this sequence is infinite; can this be proved unconditionally? The averaged result of Bombieri-Friedlander-Iwaniec does not seem to be strong enough.
%H A180362 Charles R Greathouse IV, <a href="b180362.txt">Table of n, a(n) for n = 1..10000</a>
%H A180362 D. R. Heath-Brown, "<a href="http://eprints.maths.ox.ac.uk/166/">Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression</a>", Proceedings of the London Mathematical Society 64:3 (1992), pp. 265-338.
%F A180362 k * n^n + 1, where k < n^n.
%e A180362 a(4) = 109, because 4 * 3^3 + 1 = 109, which is prime, and 4 < 27.
%o A180362 (PARI) isA180362(n)=my(b=2);while(b^b<n,if(n%(b^b)==1 && n < b^(2*b), return(isprime(n)));b++);0
%K A180362 nonn,new
%O A180362 1,1
%A A180362 Kevin Batista (kevin762401(AT)yahoo.com), Aug 30 2010[/code]

CRGreathouse 2010-09-01 14:54

[QUOTE=3.14159;228031]Yes, yes, I'm working on the sequence's b-file. Unless Charles decided to hinder my efforts by sending it first.[/QUOTE]

I told you in #1246 I already had it...

3.14159 2010-09-01 14:57

[QUOTE=CRGreathouse]I told you in #1246 I already had it...
[/QUOTE]

Not to worry, I only submitted the corrections. I never sent the b-file.

Also: Made sequence A175768 for the sequence with no restriction on k, meaning the 4n + 1 primes are a subset of the sequence, and my guess on how much of the sequence are 4n + 1 primes = 85 to 99 percent.

I have the members of this sequence up to 4k.

CRGreathouse 2010-09-01 14:58

[QUOTE=3.14159;228033]I'll work on the sequence, with no restriction. In this case, b > 1. (This means the set of 4n + 1 primes is a subset of this sequence.)[/QUOTE]

When you submit that sequence, you may wish to include its relative density in the primes (you can probably work this out, or else find my post where I give it) and cross-references (at least to A180362).


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