# An Early Christmas Algebraic Sequence

**Number Theory**Level 5

Consider the sequence \({ a }_{ 1 },{ a }_{ 2 },{ a }_{ 3 },{ a }_{ 4 },\dots\) such that \({ a }_{ 1 }=2\) and for every positive integer \(n\),

\({ a }_{ n+1 }={ a }_{ n }+{ p }_{ n }\) , where \({ p }_{ n }\) is the largest prime factor of \({ a }_{ n }\).

The first few terms of the sequence are \(2,4,6,9,12,15,20\). What is the largest value of \(n\) such that \({ a }_{ n }\) is a four-digit number?

**Note**: This is adapted from a Mathematics competition. Happy solving; From
Issac Newton,

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.