My interpretation of the problem is not just to find 3 consecutive primes such that the two gaps are the same, but also that these will be the first and second instances of that particular prime gap size.

So, for example 23 to 29 is the first instance of a gap of 6.  But it is followed by 31 and a gap of 2.  So the first prime gap of 6 is not followed by another gap of 6.

My solution:

3 primes         2 gaps

3 5 7                 2 2

199 211 223    12 12

----------

import sympy as s

gaps = {}

prior = 2

for n in range(10000):

    new = s.nextprime(prior)

    gap = new - prior

    if gap not in gaps:

        future = s.nextprime(new)

        futuregap = future - new

        gaps[gap] = [new, futuregap]

        if gap == futuregap:

            print(prior, new, future, '  ', gap, futuregap)

    prior = new