Twenty-four UMass Lowell students competed in the 2015 William Lowell Putnam Mathematics Competition on Saturday, December 5. The competition took place concurrently throughout the US and Canada. Normally, around 5,000 students compete each year. There were two 3 hour sessions, each with six problems. As usual, the problems were tough. The consensus of students at the end was that this was the easiest.

Given a list of the positive integers 1, 2, 3, 4, …, take the first three numbers 1,2,3 and their sum 6 and cross all four numbers off the list. Repeat with the three smallest remaining numbers 4, 5, 7 and their sum 16. Continue in this way, crossing off the three smallest remaining numbers and their sum, and consider the sequence of sums produced: 6, 16, 27, 36,…. Prove or disprove that there is some number in this sequence whose base 10 representation ends with 2015.