Browse · MATH
Printjmc
number theory senior
Problem
The sequence 12, 15, 18, 21, 51, 81, consists of all positive multiples of 3 that contain at least one digit that is a 1. What is the term of the sequence?
Solution
We know that the rule for divisibility by is that the digits of the number must add up to a multiple of . So, it's clear that there are no other such two-digit numbers beyond the ones listed in the problem. Every number divisible by between and is in the sequence, so that gets us through the th term of the sequence. Using the rule for divisibility by , it is fairly simple to list out the remaining terms of the sequence: . Thus, the th term is .
Final answer
318