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)