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OBM 2000 Problem 3

    Define ff on the positive integers by f(n)=k2+k+1f(n) = k^2 + k + 1 , where n=2k(2l+1)n=2^k(2l+1) for some k,lk,l nonnegative integers. Find the smallest nn such that f(1)+f(2)+...+f(n)≥123456f(1) + f(2) + ... + f(n) \geq 123456 .

    Dataset text AI-MO AoPS. Quoted with source.

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