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Sequence determined by indices condition

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November 1, 2010
number theory unsolvednumber theory

Problem Statement

Suppose that a sequence (an)n=1∞(a_n)_{n=1}^{\infty} of integers has the following property: For all nn large enough (i.e. n≥Nn \ge N for some NN ), ana_n equals the number of indices ii, 1≤i<n1 \le i < n, such that ai+i≥na_i + i \ge n. Find the maximum possible number of integers which occur infinitely many times in the sequence.
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