MathDB

For any odd positive integer

n

, let

r(n)

be the odd positive integer such that the binary representation of

r(n)

is the binary representation of

n

written backwards. For example,

r(2023)=r(111111001112)=111001111112=1855

. Determine, with proof, whether there exists a strictly increasing eight-term arithmetic progression

a_1, \ldots, a_8

of odd positive integers such that

r(a_1), \ldots , r(a_8)

is an arithmetic progression in that order.

Problem Statement