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#78a0ce6a-081e-40a5-8398-bb83e630cfc6中等填空题数列的基本概念数列

14.(2023•海淀区校级三模)已知数列{an}\{a_{n}\}满足:对任意的nNn\in N^{*},总存在mNm\in N^{*},使得Sn=amS_{n}=a_{m},则称{an}\{a_{n}\}为"回旋数列".以下结论中正确的个数是((  ))
①若an=2023na_{n}=2023n,则{an}\{a_{n}\}为"回旋数列";
②设{an}\{a_{n}\}为等比数列,且公比qq为有理数,则{an}\{a_{n}\}为"回旋数列";
③设{an}\{a_{n}\}为等差数列,当a1=1a_{1}=1d<0d<0时,若{an}\{a_{n}\}为"回旋数列",则d=1d=-1
④若{an}\{a_{n}\}为"回旋数列",则对任意nNn\in N^{*},总存在mNm\in N^{*},使得an=Sma_{n}=S_{m}