A048554 p(n+1) is next smallest prime beginning with p(n), initial prime is 13.
13, 131, 1319, 131909, 13190909, 1319090933, 131909093341, 13190909334101, 1319090933410141, 131909093341014131, 13190909334101413129, 131909093341014131297, 13190909334101413129739
Offset: 0