Prove the existence of a natural number divisible by $q=2p+1$, where $q,p$ are primes, such that the sum of the digits is at most $3$

Question

Prove the existence of a natural number divisible by $q=2p+1$, where $q,p$ are primes, such that the sum of the digits is at most $3$.

The digit sum is supposed to be equal to or less than $3$ in the decimal system. I thought about using the formula for digit sum $$\sum_{n=0}^{| \log_{10} x |} 10^{-2} (x \bmod 10^{n+1} - x \bmod 10^n)$$ and then expressing the appropriate variables but I can't get any further than that. Is this even the right way to go?