Let $a_{1} = 1$ and $a_{2} = 2$ and for $k \geq 3$ choose $a_{k}$ to be the least integer $> a_{k - 1}$ which is the sum of at least two consecutive terms of the sequence. What is the asymptotic behaviour of this sequence?

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number theory · open · 0 attempts

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gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is **Hofstadter’s “consecutive-sum” greedy sequence**, listed as **OEIS A005243**. It was posed by Hofstadter and recorded by Erdős (who explicitly asked for its asymptotic behaviour).

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llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

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oeis

A005243 — A self-generating sequence: start with 1 and 2, take all sums of any number of successive previous elements and adjoin them to the sequence. Repeat!1,2,3,5,6,8,10,11,14,16,17,18,19,21,22,24,25,29,30,32,33,34,35,37,40,41,43,45,46,47,49,51,54,57,58,59,60,62,65,67,68,69,

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