MathDB
2013 HMMT Guts #18: Multi-Base Recursion

Source:

March 26, 2013
HMMT

Problem Statement

Define the sequence of positive integers {an}\{a_n\} as follows. Let a1=1a_1=1, a2=3a_2=3, and for each n>2n>2, let ana_n be the result of expressing an−1a_{n-1} in base n−1n-1, then reading the resulting numeral in base nn, then adding 22 (in base nn). For example, a2=310=112a_2=3_{10}=11_2, so a3=113+23=610a_3=11_3+2_3=6_{10}. Express a2013a_{2013} in base 1010.
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