To form the sequence, write the primes 2, 3, 5, 7,... as an infinite string 2357111317...; then take the first 2 digits of the string, 23, then the next 3 digits, 571, then the next 5 digits, 11317, then the next 7 digits, 1923293, then... (stepping through prime numbers of digits). Omit any leading 0's.

A043347

To form the sequence, write the primes 2, 3, 5, 7,... as an infinite string 2357111317...; then take the first 2 digits of the string, 23, then the next 3 digits, 571, then the next 5 digits, 11317, then the next 7 digits, 1923293, then... (stepping through prime numbers of digits). Omit any leading 0's.