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Old 2020-02-10, 03:00   #4
CRGreathouse
 
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Aug 2006

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Quote:
Originally Posted by fivemack View Post
Prove there is no integer for which n, 2n, 4n, ..., (2^20)n all have no 0 in their decimal expansion
Nicely done.

Quote:
Originally Posted by fivemack View Post
Find an integer for which n, 2n, 4n, ..., (2^19)n all have no 0 in their decimal expansion
I believe 348612479 will do. My search code:

Code:
has(n)=vecmin(digits(n))>0
is(n)=for(k=1,19,if(!has(n<<k),return(0)));1
for(N=1,9^8, n=fromdigits(digits(N,9)); k=n%10; if((k==2||k==7) && is(10*n+9), return(10*n+9)))
No doubt this could have been done more efficiently.
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