6300846559 is such that 6 is divisible by 2; 63, by 3; 630, by 5; 6300, by 7; and, in general, if you take its first N digits, it will be divisible by the N-th prime.

There is only one other such 10 digit number: can you find it?

I did this by hand calculator only (1 hour elapsed time) and found every number of every length.

There are four one digit numbers that work where we might expect 9/2 = 4.5

There are 13 two digit numbers.  Expected 99/(2*3) = 16.5

26 three digit and 999/(2*3*5) = 33.3

43 four digit and 9999/(2*3*5*7) = 47.61

39 five digit and (10^5 - 1)/(2*3*5*7*9) = 43.29

33 six digit expect 33.3

23 seven digit expect 19.59

10 eight digit expect 10.31

4 nine digit expect 4.48

2 ten digit expect 1.55

0 eleven digit expect .4986

 

Posted by Jer on 2005-01-04 18:20:26