Non-additive-subtractive prime sequence Call the following a NON additive-subtractive prime sequence or lets name it Gary's sequence. It goes like this: let a(0)=2. The next term is defined as smallest prime number which cannot be expressed as the sum and/or difference of any previous terms (note that it means using any combination of plus and minus signs and any number of previous terms).
The sequence begins: 2, 3, 7, 11, 29, 53, 107,...
this sequence is infinite.
My question is: 

Can you describe the behavior of this sequence or maybe you can even create a formula for generating this?

(Remember you are allowed to use each prime exactly once and repetition like 2+2+3+7+11 is absolutely not allowed). For example, 17 is not a member of this sequence because 17 can be expressed as 11+2+7-3 . Also 83 is not a member of this sequence since 83 can be expressed as 11+29-3-7+53 . Also 47 is not a member of this sequence because 47 can be expressed as 29+7+11)

This seems identical to: 
OEIS A138000 "Least prime such that the subsets of { a(1),...,a(n) } sum up to 2^n different values."
http://oeis.org/A138000
Discovered by S. J. Benkoski and P. Erdos, On weird and pseudoperfect numbers, Math. Comp. 28 (1974) 617-623
You're following in the footsteps of giants ;-)
Your next term should be a(8) = 211 (not 157 = 107+29+11+7+3)
As to the closed-form, OEIS says: 

a(n) > a(n-1) and a(n) <= nextprime(sum(a(i),i=1..n-1)-(-1)^n) ; but
  in fact a(n) ~ sum(a(i),i=1..n-1)
and thus a(n) ~ constant*2^n

where constant >~ 1.6739958...
It's probably safest to define a(n) using nearestprime() rather than nextprime(), to avoid precision issues for large n.
As to the name, Benkoski and Erdos didn't give this sequence a name... but I don't think you can call it Gary's sequence.
