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Any number can be written as the sum of two terms in the seq

Source: Spanish Mathematical Olympiad 2013. Problem 5.

March 26, 2015

Integer sequencenumber theory

Problem Statement

Study if it there exist an strictly increasing sequence of integers

0=a_0<a_1<a_2<...

satisfying the following conditions

i)

Any natural number can be written as the sum of two terms of the sequence (not necessarily distinct).

ii)

For any positive integer

n

we have

a_n > \frac{n^2}{16}