Doubling numbers

Number Theory Level pending

What is the 2017th smallest positive integer that gains a digit when doubled?

For example, 57 is one such integer, because it has two digits, and when doubled, 57 × 2 = 114 57\times 2=114 has 3 digits.


The answer is 6461.

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1 solution

5,6,7,8,9—one digit number —5 numbers 50,51…….......99-two digit numbers-50 numbers 500,501.........999- three digit numbers-500 numbers 1462 numbers are left now numbers will be counted from 5000 So 1462th number from 5000 is 6461.

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