#JavaScript (ES6), 60 bytes

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    f=(n,k=n*++n/2)=>k>9?f(!n,eval([...k+''].join('*+'[+!n]))):k

[Try it online!](https://tio.run/##FY5BboMwFET3PYWzsh1PXX@DAyQyXfUUiIVFoE1A31US5fokjDSLp9GT5pqe6T7cLv@PT87ncV2nqBhz5L0x/OV1bOe2@Z7UjjE@06I6a@1spOztNV9Yyb2Rndlxr7U@zuup8yhQIuCACjUakAMRyIMKUAkKoAOoAtWgBt7Bb2tRonAuIDhXoQp1uYlb@g875dtPGv4Ui9iKIfM9L6Nd8q@SSUlhBL8rtYhig0nx@8n6Ag "JavaScript (Node.js) – Try It Online")