counting expressions (a/b +- c/d)

[wouter meeussen]

I should have said:
... where a,b,c,d are integers or square roots of  *primes*  ...
2, 115, 1471, 7065, 30215, 66303, 198286     for n= 1...7

using
Table[v=Sort[Join[Range[i], Sqrt[Prime[Range[PrimePi[i^2]]]]], OrderedQ[N@
{#1, #2}] &]; Length@ Union[Simplify@ Abs[Flatten@ {Outer[#1/#2 + #3/#4 &,
v, v, v, v],
Outer[#1/#2 - #3/#4 &, v, v, v, v]}]], {i, 7}]

W.

----- Original Message ----- 
From: "wouter meeussen" <wouter.meeussen at pandora.be>
To: "Seqfan (E-mail)" <seqfan at ext.jussieu.fr>
Sent: Saturday, May 13, 2006 3:19 PM
Subject: counting expressions (a/b +- c/d)


> hi All,
>
> what is the proper name of expressions r = (a/b +- c/d) where a,b,c,d are
> integers or square roots of integers?
> Their count a[n]  of  non-negative r given the a,b,c,d have values <= n is
> 2, 115, 1471, 7065, 30215, 66303     for n= 1...6
> nothing on superseek.
> Anyone care to extend or to suggest pointers / links?
>
> W.
>