Let M_n = A002110(n) (the n-th primorial), let N*(n)(N**(n), respectively) be the number of numbers k in [1, M_n] for which lpf(k-3) > lpf(k-1) >= prime(n) (lpf(k-1) > lpf(k-3) >= prime(n), respectively) such that k-3, k-1 are not twin primes, where lpf=least prime factor. Then a(n) = N*(n) - N**(n).

A242974

Let M_n = A002110(n) (the n-th primorial), let N*(n)(N**(n), respectively) be the number of numbers k in [1, M_n] for which lpf(k-3) > lpf(k-1) >= prime(n) (lpf(k-1) > lpf(k-3) >= prime(n), respectively) such that k-3, k-1 are not twin primes, where lpf=least prime factor. Then a(n) = N*(n) - N**(n).