2n

The first powers of 2 are :
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512
210 = 1024

They begin by the digits 1,2,3,4,5,6 or 8.

Smallest power of 2 beginning by a 7 ? a 9 ?
Solution

It can be shown that for any number n, there is a power of 2 beginning by the digits of n.
Smallest power of 2 beginning by 100 ? by 1000 ? by 123456789 ?
Solution

Details

 

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