I'm working with the Zeckendorf representation of prime numbers. I'm using
ResourceFunction["ZeckendorfRepresentation"][Prime[n]]
and I would like to select from all the results, the ones with this peculiar representation: an alternating sequence of $ 1 $ and $ 0 $ of various lenght, ending with two adjacent $ 0 $ and $ 1 $ (and eventually just various $ 0 $). As an example I want to select $ 607 $ because this is the representation:
$ \{1,0,1,0,1,0,1,0,1,0,0,1,0\} $
or $ 6763 $:
$ \{1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1\} $
Or $ 679891411787178541 $
$\{1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\}$