Mathegoras

Sequences and series › Recursive sequences › Computing terms of a recurrence

Possible second terms of a sequence

High school · ●●●●○ 100 pts

A sequence a1,a2,…a_1, a_2, \ldots of non-negative integers is defined by the rule an+2=∣an+1−an∣a_{n+2}=|a_{n+1}-a_n| for n≥1n\geq1. If a1=999a_1=999, a2<999a_2<999, and a2006=1a_{2006}=1, how many different values of a2a_2 are possible?

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