10 for x=1 to 20
20     ?x,(2^x)@x
30 next

finds this sequence

1       0
2       0
3       2
4       0
5       2
6       4
7       2
8       0
9       8
10      4
11      2
12      4
13      2
14      4
15      8
16      0
17      2
18      10
19      2
20      16

Putting the terms into Sloane's  The On-Line Encyclopedia of Integer Sequences! gives sequence A015910, which links to A050259 to list the x values that lead to a remainder of 3. That sequence starts 1, 4700063497, 3468371109448915, 8365386194032363, meaning that in the current context, 4,700,063,497 is the answer.