Take a prime p and concatenate it with the next prime after p, q. If the result p||q is prime then take p+q and concatenate the sum to the next prime after q, r. If the result (p+q)||r is prime then take p+q+r and concatenate it to the next prime (s) after r, getting (p+r+r)||s, and so on. a(n) is the least prime for which this process continues for n steps.

A333935

Take a prime p and concatenate it with the next prime after p, q. If the result p||q is prime then take p+q and concatenate the sum to the next prime after q, r. If the result (p+q)||r is prime then take p+q+r and concatenate it to the next prime (s) after r, getting (p+r+r)||s, and so on. a(n) is the least prime for which this process continues for n steps.