hard or easy ? more, please...

[Maximilian Hasler]

>   Is there any significance to these p,q s?
> (That is, is there any reason you really want these to be primes?)

Well, I was looking for some "primitive" solutions, but...
maybe it's a good idea to drop this in a first approach !

>   With the same relationship but allowing {p,q} to be any pair of odd
>  numbers, you only seem to come across a couple of more pairs:
>  {3,3} (also solves your prime case)
yes, I realized I forgot to mention this one (only possible case with p=q)

>  {3,21}
>  {7,73}
>  {21, 507}
>  {73, 793}
>  {793, 8647}
>
>  What's interesting about this are the sequence of pairs:
>  {7,73} {73, 793}, {793, 8647} ... ?

{1,7}...{8647,94321}...

oh yes, I see :
a(n+1) = 11 a(n) - a(n-1) - 3, a(0)=a(1)=1:

? a=[1,1];for(n=2,10,a=concat(a,11*a[n]-a[n-1]-3));a
%51 = [1, 1, 7, 73, 793, 8647, 94321, 1028881, 11223367, 122428153, 1335486313]

? pq(1028881, 11223367)
%52 = [1028881, 11223367, 0, 0]
? ?pq
pq(p,q)=[p,q,((p+1)*(p+2)+1)%q,((q+1)*(q+2)+1)%p]

Thanks a lot! I'll see what this will give in my original problem...

Maximilian