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a_n=1234567891011 ...n is not divisible by 3 (Chile 2016 L2 P1)

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October 22, 2022
number theorydivisible

Problem Statement

The natural number ana_n is obtained by writing together and ordered, in decimal notation , all natural numbers between 11 and nn. So we have for example that a1=1a_1 = 1,a2=12a_2 = 12, a3=123a_3 = 123, .... . . , a11=1234567891011a_{11} = 1234567891011, ...... . Find all values of nn for which ana_n is not divisible by 33.
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