PARI's commands

[3.14159]

Originally Posted by science_man_88

it's up, and doesn't look like he did.

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]

Originally Posted by 3.14159

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!

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

(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,

[science_man_88]

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

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

[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.

[3.14159]

Originally Posted by 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.

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]

Originally Posted by 3.14159

Yes, yes, I'm working on the sequence's b-file.

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

[3.14159]

Originally Posted by science_man_88

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

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]

Here's what I submitted:

%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

[CRGreathouse]

Originally Posted by 3.14159

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

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

[3.14159]

Originally Posted by CRGreathouse

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

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]

Originally Posted by 3.14159

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.)

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).