Is there an efficient program for generating a Sidon sequence? I would need a Sidon sequence of about $10^9$ elements.
I found math papers like [1] that explain how to generate Sidon sequences but it seems a lot of pain to write the corresponding program.

Are you aware of any existing program that generates a dense enough and large enough Sidon sequence ?

Extra: my real constraint for the sequence is $a+a′ , a \lt a′ ,~ a,a′ ∈ A$ instead of the true Sidon sequence property $a+a ′ , a ≤ a ′ , a, a ′ ∈ A$.
So a Sidon sequence would do the job but I could hope for a denser sequence by tuning the program. 

[1] Javier Cilleruelo, "Infinite Sidon sequences", eprint on arXiv: http://arxiv.org/abs/1209.0326
Consider a prime $p$ and let $g$ be a primitive root mod $p$. The set $ A= \{ (x,g^{x}), x=0,..,p-2\}$ is a Sidon set in $Z_{p-1} \times Z_{p}$. This is an explicit method. 

Now, since $Z_{p-1} \times Z_{p}$ is isomorphic to $Z_{p(p-1)}$, then the natural isomorphism $\Phi$ maps $A$ in $\Phi(A)$, which is also a Sidon set in $Z_{p(p-1)}$, which is a Sidon set in $[1,p(p-1)]$.