A054697 3 consecutive primes differ by 2n or more starting at a(n).

3, 19, 47, 199, 199, 199, 1831, 2161, 2161, 3947, 16007, 16007, 24251, 24251, 24251, 38461, 38461, 38461, 38461, 38461, 58789, 203669, 206651, 206651, 413299, 413299, 413299, 1272679, 1272679, 1272679, 1272679, 2198909, 2198909, 2198909