Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits.
Consider the set E of all natural numbers n such that when divided by 11,12,13 respectively, the remainders, in that order, are distinct prime numbers in an arithmetic progression. If N is the largest number in E, find the sum of digits of N.
But try the problem first...
Answer: is No largest value.
PRMO, 2019, Question 20
Elementary Number Theory by David Burton
here N can be of the form (13)(12)(11)(k)+29
where k belongs to an integer
then no largest value.