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Cubing digits sequence

Source:

November 17, 2005
modular arithmeticalgebraAMC 10recursionSequences

Problem Statement

The first term of a sequence is 2005. Each succeeding term is the sum of the cubes of the digits of the previous terms. What is the 2005th term of the sequence? <spanclass=latexbold>(A)</span> 29<spanclass=latexbold>(B)</span> 55<spanclass=latexbold>(C)</span> 85<spanclass=latexbold>(D)</span> 133<spanclass=latexbold>(E)</span> 250 <span class='latex-bold'>(A)</span>\ 29\qquad <span class='latex-bold'>(B)</span>\ 55\qquad <span class='latex-bold'>(C)</span>\ 85\qquad <span class='latex-bold'>(D)</span>\ 133\qquad <span class='latex-bold'>(E)</span>\ 250