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   Author  Topic: Curious numbers  (Read 695 times)
FiBsTeR
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Curious numbers  
« on: Jul 7th, 2018, 6:26am »
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A k-curious number is a positive integer s such that when you multiply s by k, you get s except with the right-most digit moved to the left.
 
For example, the smallest 4-curious number is 102564 because:
102564 * 4 = 410256
 
The smallest 5-curious number is 142857 because:
142857 * 5 = 714285
 
What is the smallest 6-curious number?
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towr
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Re: Curious numbers  
« Reply #1 on: Jul 7th, 2018, 12:23pm »
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It seems to be 1016949152542372881355932203389830508474576271186440677966  
 
Say we're trying to find the number N = 10M+D where D is a digit and M a natural number
We want 6*(10M+D) = D*10^K + M, where K is the number of digits in M
Simplify this to 59*M = (10^K-6)*D
And now you can do a much more targeted search than running through every number: D is limited to 9 choices, and we can just try increasing K
 
#python-code
for K in range(100):
 for D in range(1,10):
  X = (10**K-6)*D
  if X % 59 == 0:
   M = X//59
   if len(str(10*M+D)) == len(str(D*10**K + M)):
    print((10*M+D), '-', D*10**K + M)
« Last Edit: Jul 7th, 2018, 12:25pm by towr » IP Logged

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towr
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Re: Curious numbers  
« Reply #2 on: Jul 7th, 2018, 12:32pm »
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Wikipedia calls these parasitic numbers
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FiBsTeR
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Re: Curious numbers  
« Reply #3 on: Jul 9th, 2018, 7:34am »
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Nice, that's right!
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