MathDB

For each positive integer

k,

let

t(k)

be the largest odd divisor of

k.

Determine all positive integers

a

for which there exists a positive integer

n,

such that all the differences

t(n+a)-t(n); t(n+a+1)-t(n+1), \ldots, t(n+2a-1)-t(n+a-1)

are divisible by 4.
Proposed by Gerhard Wöginger, Austria

Problem Statement