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Scott Cram Inner circle 2678 Posts 
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Playing around with the base 10 logarithms of powers of 2, I noticed an amusing pattern.
Here are the base 10 logarithms of the first 20 powers of 2. Notice the first digit to the right of the decimal point of each logarithm. They go in a very familiar pattern: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0, then it repeats. Does that pattern seem familiar to anyone or everyone?  |
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vindar New user Paris, France 62 Posts
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Hi,
Indeed, this is fun 
The explanation is that log(10)/log(2) = 0.301... is close to 0.3. In this case, the sequence will fail after n=100. If you take the first digit after the decimal point of the (simpler) sequence n*0.3 then the pattern will repeat infinitely: http://www.wolframalpha.com/input/?i=Tab......2C+100}]. |
Michael Daniels Inner circle Isle of Man 1627 Posts
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The last digit of successive multiples of 3 immediately springs to mind.
Mike |
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Scott Cram Inner circle 2678 Posts
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Quote:
On Apr 6, 2014, vindar wrote: I'm familiar with why it works, but I just found it amusing, as I never thought about it that way before. Quote:
On Apr 6, 2014, Michael Daniels wrote: Michael, you're a true mathematician! |
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Michael Daniels Inner circle Isle of Man 1627 Posts
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Too kind, Scott!
It's also interesting that this repeating sequence is the exact reverse of that obtained when considering the last digit of successive multiples of 7. 7,4,1,8,5,2,9,6,3,0, ... Mike |
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Posted: Apr 6, 2014 06:28 pm 
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