MathDB

Given a list of the positive integers

1,2,3,4,\dots,

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, \dots.

Prove or disprove that there is some number in this sequence whose base 10 representation ends with

2015.

B2