In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any n > 2 define an to be the smallest integer greater than an?1 which can not be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns.
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