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# counting problem

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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.

Aug 5, 2022

#1
+124707
+2

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

Aug 5, 2022
edited by CPhill  Aug 6, 2022
#2
+2602
0

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.

Aug 6, 2022
#3
+113
+1

Python 3.9 says: 2, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288

But NOT 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144

Python also says \(2^{19} = 524,288\)

tuffla2022  Aug 6, 2022
edited by tuffla2022  Aug 6, 2022
edited by tuffla2022  Aug 6, 2022