2015 Putnam B2

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 the sequence whose base 10 representation ends with $2015$.

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给定一个正整数列表 $1,2,3,4,\dots$，取前三个数字

$1,2,3$ 及其总和 $6$，然后将所有四个数字从列表中划掉。与三个重复

剩余的最小数字 $4,5,7$ 及其总和 $16$。继续以这种方式，划掉剩余的三个最小数字及其总和，并考虑产生的总和的序列：$6, 16, 27, 36, \dots$。证明或反驳序列中存在某个数字，其基数 10 表示以 $2015$ 结尾。

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