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Infinite sequence of integers

Source: Cono Sur 2010 #6

November 17, 2015
number theorycono sur

Problem Statement

Determine if there exists an infinite sequence a0,a1,a2,a3,...a_0, a_1, a_2, a_3,... of nonegative integers that satisfies the following conditions: (i) All nonegative integers appear in the sequence exactly once. (ii) The succession bn=an+n,b_n=a_{n}+n,, n≥0n\geq0, is formed by all prime numbers and each one appears exactly once.
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