What is the smallest pair (a_{1},a_{2}) of integers (a_{1}, less than a_{2}) to provide a list of 24 integers using a recurrent function a_{(n)}=(a_{(n-1)}+a_{(n-2)})/2?
The key is that both starting numbers be divisible by 2^22. So you can just use a1=0 and a2=2^22. a1=0 a2=2^22 = 4194304 a3=2^21 a4=2^21 + 2^20 a5=2^21 + 2^19 a6=2^21 + 2^19 + 2^18 ... a23=2^21 + 2^19 + 2^17 + ... + 2^1 a24=2^21 + 2^19 + 2^17 + ... + 2^1 + 2^0 = 2796203