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Beautiful sequence (help)

Source: 26 Australian-Polish Mathematic Competition 2003

December 15, 2005
algebra unsolvedalgebraSequence

Problem Statement

The sequence a0,a1,a2,..a_0, a_1, a_2, .. is defined by a0=a,an+1=an+L(an)a_0 = a, a_{n+1} = a_n + L(a_n), where L(m)L(m) is the last digit of mm (eg L(14)=4L(14) = 4). Suppose that the sequence is strictly increasing. Show that infinitely many terms must be divisible by d=3d = 3. For what other d is this true?
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