Combinatorics and Graph Theory

    

Asymptotic Behavior of the Erdos Consecutive Sum Sequence A003462

Authors: Jehan Singh

We study the self-generating consecutive-sum greedy sequence (an)n ≥ 1, defined by a1 = 1, a2 = 2, and for k ≥ 3, ak is the least integer greater than ak−1 expressible as a sum of at least two consecutive earlier terms. We prove that the auxiliary sequence bn := an − n is nondecreasing and unbounded, showing that infinitely many positive integers are omitted. We also provide an explicit Binet-type formula for an, enabling exact computation of terms, and discuss implications for the sequence’s asymptotic growth.

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[v1] 2026-03-11 20:25:37

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