MathDB

For how many pairs of sequences of nonnegative integers

(b_1,b_2,\ldots, b_{2018})

and

(c_1,c_2,\ldots, c_{2018})

does there exist a sequence of nonnegative integers

(a_0,\ldots, a_{2018})

with the following properties:
[*] For

0\leq i\leq 2018,

a_i<2^{2018}.

[*] For

1\leq i \leq 2018, b_i=a_{i-1}+a_i

and

c_i=a_{i-1}|a_i

;
where

|

denotes the bitwise or operation?

Problem Statement