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prove the seventh term is not prime in a recursive sequence

Source: Czech and Slovak third round,2006,p1

March 3, 2012
number theory proposednumber theory

Problem Statement

Define a sequence of positive integers {an}\{a_n\} through the recursive formula: an+1=an+bn(n≥1)a_{n+1}=a_n+b_n(n\ge 1),where bnb_n is obtained by rearranging the digits of ana_n (in decimal representation) in reverse order (for example,if a1=250a_1=250,then b1=52,a2=302b_1=52,a_2=302,and so on). Can a7a_7 be a prime?
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