MathDB

For a sequence

a_1<a_2<\cdots<a_n

of integers, a pair

(a_i,a_j)

with

1\leq i<j\leq n

is called interesting if there exists a pair

(a_k,a_l)

of integers with

1\leq k<l\leq n

such that

\frac{a_l-a_k}{a_j-a_i}=2.

For each

n\geq 3

, find the largest possible number of interesting pairs in a sequence of length

n

Problem Statement