Determine the largest integer A such that for K=1,2,3,...,length(A) the first K digits of A form an integer divisible by K.
For example, for 56165, 5 is divisible by 1, 56 is divisible by 2, 561 is divisible by 3, 5616 is divisible by 4 and 56165 is divisible by 5.
(In reply to
Solution by Larry)
A simple formula for the number of length A numbers is n(A)=(10^A)/(A!)
The numbers underperform expectation for all n up to n(14)=1147.07
after that, there are more numbers than predicted from n(15)=764.72
through n(25)=0.64
n(26)=0.25 was large enough that I'd hoped maybe there might just be one before seeing the previous posts.
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Posted by Jer
on 2024-04-28 10:23:17 |
Comparison to expectation
