MathDB

perfect square belonging to an integer sequence

Source: Nordic Mathematical Contest 2013 #1

September 23, 2017

floor functionPerfect Squarenumber theoryInteger sequence

Problem Statement

Let

{(a_n)_{n\ge1}}

be a sequence with

{a_1 = 1}

and

{a_{n+1} = \lfloor a_n +\sqrt{a_n}+\frac{1}{2}\rfloor }

for all

{n \ge 1}

, where

{\lfloor x \rfloor}

denotes the greatest integer less than or equal to

{x}

. Find all

{n \le 2013}

such that

{a_n}

is a perfect square