Roble number I

Number Theory Level 3

A roble number is a positive integer that does not contain any of the digits 1, 4, and 3. The first few roble numbers are 2, 5, 6, 7, 8, 9, 20, 22, 25.... What is the 2018th roble number ?

Related Problems: You might also want to try Roble Problem II and Roble Problem III .


The answer is 8925.

Jeffrey Robles by Jeffrey Robles , 26, Ireland

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1 solution

Chew-Seong Cheong
Jul 25, 2018

The roble number is a base-7 number system with 0 r → 0 7 0_r \to\ 0_7 , 2 r → 1 7 2_r \to\ 1_7 , 5 r → 2 7 5_r \to\ 2_7 , 6 r → 3 7 6_r \to\ 3_7 , 7 r → 4 7 7_r \to\ 4_7 , 8 r → 5 7 8_r \to\ 5_7 , and 9 r → 6 7 9_r \to\ 6_7 .

Therefore the 2018th roble number is:

201 8 10 = 561 2 7 = 8925 r 2018_{10}=5612_7=\boxed{8925}_r

3 Helpful 0 Interesting 1 Brilliant 0 Confused

Can you tell me how you came up with the solution? was it an observation or you had some prior knowledge? In case there is a text about it,I would appreciate if you had shared it with me. Cheers

A Former Brilliant Member - 2 years, 10 months ago

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Sorry, no prior knowledge nor text.

Chew-Seong Cheong - 2 years, 10 months ago

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