counting problem

Question

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How many positive integers smaller than 1,000,000 are powers of 2, but are not powers of 4? You may find it useful to consider that 2^10 = 1024.

Guest Aug 5, 2022

CPhill · Answer 1 · 2022-08-05T11:42:33

Any

2^(2n - 1) will not be an integer power of 4

When n = 1, 2^(2n-1) = 2^1 = 2

When n = 10, 2^(2*10 - 1) = 2^19 = 524,888

So

10 are integer powers of 2 but not powers of 4

BuilderBoi · Answer 2 · 2022-08-06T12:12:29

The number must have an odd power.

So, the exponents can be 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, which makes for \(\color{brown}\boxed{10}\) numbers.