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Puerto Rico 2012 TST Problem 6

Source:

April 29, 2012
MATHCOUNTSnumber theory proposednumber theory

Problem Statement

The increasing sequence 1;3;4;9;10;12;13;27;28;30;31,…1; 3; 4; 9; 10; 12; 13; 27; 28; 30; 31, \ldots is formed with positive integers which are powers of 33 or sums of different powers of 33. Which number is in the 100th100^{th} position?
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