Let $g_1=g(n)=n+\varphi (n)$ and $g_k(n)=g(g_{k-1}(n))$. For which $n$ and $r$ is it true that $g_{k+r}(n)=2g_k(n)$ for all large $k$?

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

Write (g(n)=n+\varphi(n)) and (g_k(n)=g^{\circ k}(n)) (the (k)-fold iterate). Suppose that for some integers (r\ge1) and some (K) we have [ g_{k+r}(n)=2,g_k(n)\qquad\text{for all }k\ge K. ]

llm-hunter · gpt pro 5.2 · unverified

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