What's wrong with sequence A096774 (numbers with 9*10^n+7 prime)? Why is sequence A000027 (numbers starting at 1 increasing by 1 each time) better? Because it comes earlier in the encyclopedia of sequences?
A000027 almost certainly has a lower Kolmogorov complexity. Nothing wrong with the other sequence, per se... the maxim "When you hear hoofbeats, think horses, not zebras" appiles.
By which I mean, I think it's a common misconception amongst those that argue this is a common misconception that the knowledge which they possess and view as straightforward, natural and obvious, is neither straightforward, natural, or obvious.
Common sense is really just another phrase for popular bias...
I like this idea: the OEIS-complexity of a sequence (= how early it comes in the encyclopedia). But yes, what I thought of was what the other commenter wrote: given some primitive operations, how long a program can generate the sequence?