x^x+n is prime: A087037, A087038

[all at abouthugo.de]

Hans, SeqFans,

Neil had asked me to submit the two sequences
proposed in my previous posting:
%S A087037 1,1,2,1,444,1,2
%N A087037 Smallest integer x>0 such that x^x+n is prime.
%C A087037 It is conjectured that all sequence terms exist. Dean
Hickerson, (dean(AT)math.ucdavis.edu).
The sequence with the unknown terms indicated by ?:
1,1,2,1,444,1,2,?,2,1,?,1,2,3,2,1,?,1,2,3,
4,1,6,?,2,3,2,1,30,1,6,3,2,3,6,1,2,5,2,1,2,1
If existing, a(8)>4011, a(11),a(17)>3874, a(24)>4097
and
%S A087038 2,3,2,3,444
%N A087038 Smallest integer x>1 such that x^x+n is prime.
%C A087038 It is conjectured that all sequence terms exist. Dean
Hickerson, (dean(AT)math.ucdavis.edu).
The sequence with the unknown terms indicated by ?:
2,3,2,3,444,?,2,?,2,3,?,5,2,3,2,3,?,19,2,3,
4,19,6,?,2,3,2,15,30,7,6,3,2,3,6,?,2,5,2,3

a(8),a(11),a(17),a(24) as indicated above, plus
a(6)>4011, a(36)>1300

Hans Havermann <hahaj at rogers.com> wrote
02.08.2003, 03:22:41:

> Hugo wrote:
> 
> > Smallest x>1 such that x^x+n is prime:
> > 2 3 2 3 444 ? 2 ? 2 3 ? 5 2 3 2 3 ? 19 2 3
> >
> > ? at n=6,8,11,17
> 
> Terms > 999 at n = {6, 8, 11, 17, 24, 36, 41, 50, 53, 59, 65, 72, 77,
[...]
> 
> > Filling the ? gaps might be a nice task:
> 
> I'll have a go at a few of these. If anyone's already working on this, 
> give me a heads-up.

If anyone wants to help filling the gaps, he
should continue searching upwards from the
starting points indicate above, which are
higher than those given in the OEIS entries.
(you have to deal with 18000++ digit numbers;
I used PFGW)

I'll be off-line for the next two weeks, so it
would be great if someone else could lead a
co-ordinated search.

Hugo