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  "body": "\n## Summary\n\nAn almost periodic sequence is a bounded sequence that comes back arbitrarily close to itself after shifts that occur regularly.\nIt need not repeat exactly.\nIt is the discrete version, in the sense of Harald Bohr, of an [[almost periodic function|GZBSV8DYGS]].\nEvery [[periodic sequence|Q3B6K9HYRG]] is almost periodic, and so is every sum of finitely many sequences $e^{i \\lambda n}$.\nAlmost periodic sequences arise as solutions of difference equations with almost periodic coefficients or forcing.\n\n## Explanations\n\n### L1 human\n\nA periodic sequence returns exactly to itself after a fixed shift.\nAn almost periodic sequence returns to within any small error you choose, and the good shifts appear at fairly regular gaps.\nThe sequence $x_n = \\cos n$ never repeats exactly, because $2\\pi$ is not a rational number.\nStill, $n \\mapsto \\cos(n + p)$ is uniformly close to $\\cos n$ whenever the integer $p$ is close to a multiple of $2\\pi$, and such integers come again and again.\n",
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