a(1) = 1 because between the first two lucky numbers (1,3) is one prime (2). a(3) = 0 because between 7 and 9 are no primes. a(6) = 2 because between 15 and 21 are two primes (17, 19).

PROG

(SageMath) [len(prime_range(A000959[i]+1, A000959[i+1])) for i in range(200)]