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Brazilian numbers (Posted on 2017-07-15) Difficulty: 3 of 5
Definition: "Brazilian" numbers ("les nombres brésiliens" in French)are numbers n such that exists a natural number k with 1<k< (n-1) such that the representation of n in base k has all equal digits.

1.Prove that all even numbers above 6 are Brazilian numbers.
2. How many odd Brazilian numbers are there below 100?

See The Solution Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: Part 1 Solution and more | Comment 2 of 4 |
(In reply to Part 1 Solution and more by Brian Smith)

Instead of searching for a specific OEIS sequence, search for the word "Brazilian".


This finds many relevant sequences, including  
A220570  Numbers that are not Brazilian.
This list starts with 1, 2, 3, 4, 5, 6, 9, 11, 17, 19, 23, 25, 29, 37, 41, 47, 49, 53, 59, 61, 67, 71, 79, 83, 89, 97.

There are 23 odd numbers below 100 that are not Brazilian, so there are 27 odd Brazilians below 100.

According to 
A257521  Odd Brazilian numbers.
they are 7, 13, 15, 21, 27, 31, 33, 35, 39, 43, 45, 51, 55, 57, 63, 65, 69, 73, 75, 77, 81, 85, 87, 91, 93, 95, 99

I take no credit for this solution, since all I did was look it up and count

Edited on July 15, 2017, 11:50 am
  Posted by Steve Herman on 2017-07-15 11:42:56

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