Count paths with prime-ending jumps

You are given an integer `n` representing the top of a staircase, where you start at step `0` and want to land exactly on step `n`. In one move, you may jump: - exactly `1` step, or - any prime number of steps whose decimal representation ends with the digit `3` (for example: `3`, `13`, `23`, `43`). Count how many distinct sequences of jumps allow you to reach step `n` exactly. Since the answer can be large, return it modulo `1,000,000,007`. A dynamic programming solution is expected. You may assume `1 <= n <= 100000`.