On integer sequences associated with admissible prime k-tuples

It is conjectured that every admissible k-tuple matches infinitely many positions in the sequence of prime numbers. The investigations of this hypothesis have led to many important results; however, the problem remains unsolved. In this work, the problem is studied from the experimental mathematics side. Integer sequences associated with the distribution of admissible prime k-tuples in the intervals (s^n; s^{n+1}] are studied experimentally, using the probabilistic Miller-Rabin primality test and parallel computing technologies. The obtained result gives us one more argument in favor of the infinitude of admissible prime k-tuples conjecture.